algebraic_topology.fundamental_groupoid.basic

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

3d7987cd

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

50251fd6

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
 -/
-import CategoryTheory.Category.Groupoid
+import CategoryTheory.Category.Grpd
 import CategoryTheory.Groupoid
-import Topology.Category.Top.Basic
+import Topology.Category.TopCat.Basic
 import Topology.Homotopy.Path
 
 #align_import algebraic_topology.fundamental_groupoid.basic from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"

50251fd6

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -115,7 +115,7 @@ def reflTransSymm (p : Path x₀ x₁) : Homotopy (Path.refl x₀) (p.trans p.sy
   prop' t x hx := by
     cases hx
     · rw [hx]; simp [refl_trans_symm_aux]
-    · rw [Set.mem_singleton_iff] at hx 
+    · rw [Set.mem_singleton_iff] at hx
       rw [hx]
       norm_num [refl_trans_symm_aux]
 #align path.homotopy.refl_trans_symm Path.Homotopy.reflTransSymm

50251fd6

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
 -/
-import Mathbin.CategoryTheory.Category.Groupoid
-import Mathbin.CategoryTheory.Groupoid
-import Mathbin.Topology.Category.Top.Basic
-import Mathbin.Topology.Homotopy.Path
+import CategoryTheory.Category.Groupoid
+import CategoryTheory.Groupoid
+import Topology.Category.Top.Basic
+import Topology.Homotopy.Path
 
 #align_import algebraic_topology.fundamental_groupoid.basic from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"

50251fd6

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
-
-! This file was ported from Lean 3 source module algebraic_topology.fundamental_groupoid.basic
-! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Category.Groupoid
 import Mathbin.CategoryTheory.Groupoid
 import Mathbin.Topology.Category.Top.Basic
 import Mathbin.Topology.Homotopy.Path
 
+#align_import algebraic_topology.fundamental_groupoid.basic from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"
+
 /-!
 # Fundamental groupoid of a space

50251fd6

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -379,7 +379,7 @@ def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd
     intro X
     change _ = (⟨_, _, _, _⟩ : FundamentalGroupoid X ⥤ FundamentalGroupoid X)
     congr
-    ext (x y p)
+    ext x y p
     refine' Quotient.inductionOn p fun q => _
     rw [← Path.Homotopic.map_lift]
     conv_rhs => rw [← q.map_id]
@@ -387,7 +387,7 @@ def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd
   map_comp' := by
     intro X Y Z f g
     congr
-    ext (x y p)
+    ext x y p
     refine' Quotient.inductionOn p fun q => _
     simp only [Quotient.map_mk, Path.map_map, Quotient.eq']
     rfl

50251fd6

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -49,6 +49,7 @@ def reflTransSymmAux (x : I × I) : ℝ :=
 #align path.homotopy.refl_trans_symm_aux Path.Homotopy.reflTransSymmAux
 -/
 
+#print Path.Homotopy.continuous_reflTransSymmAux /-
 @[continuity]
 theorem continuous_reflTransSymmAux : Continuous reflTransSymmAux :=
   by
@@ -60,6 +61,7 @@ theorem continuous_reflTransSymmAux : Continuous reflTransSymmAux :=
   intro x hx
   norm_num [hx, mul_assoc]
 #align path.homotopy.continuous_refl_trans_symm_aux Path.Homotopy.continuous_reflTransSymmAux
+-/
 
 #print Path.Homotopy.reflTransSymmAux_mem_I /-
 theorem reflTransSymmAux_mem_I (x : I × I) : reflTransSymmAux x ∈ I :=
@@ -160,11 +162,15 @@ theorem transReflReparamAux_mem_I (t : I) : transReflReparamAux t ∈ I :=
 #align path.homotopy.trans_refl_reparam_aux_mem_I Path.Homotopy.transReflReparamAux_mem_I
 -/
 
+#print Path.Homotopy.transReflReparamAux_zero /-
 theorem transReflReparamAux_zero : transReflReparamAux 0 = 0 := by norm_num [trans_refl_reparam_aux]
 #align path.homotopy.trans_refl_reparam_aux_zero Path.Homotopy.transReflReparamAux_zero
+-/
 
+#print Path.Homotopy.transReflReparamAux_one /-
 theorem transReflReparamAux_one : transReflReparamAux 1 = 1 := by norm_num [trans_refl_reparam_aux]
 #align path.homotopy.trans_refl_reparam_aux_one Path.Homotopy.transReflReparamAux_one
+-/
 
 #print Path.Homotopy.trans_refl_reparam /-
 theorem trans_refl_reparam (p : Path x₀ x₁) :
@@ -234,13 +240,17 @@ theorem transAssocReparamAux_mem_I (t : I) : transAssocReparamAux t ∈ I :=
 #align path.homotopy.trans_assoc_reparam_aux_mem_I Path.Homotopy.transAssocReparamAux_mem_I
 -/
 
+#print Path.Homotopy.transAssocReparamAux_zero /-
 theorem transAssocReparamAux_zero : transAssocReparamAux 0 = 0 := by
   norm_num [trans_assoc_reparam_aux]
 #align path.homotopy.trans_assoc_reparam_aux_zero Path.Homotopy.transAssocReparamAux_zero
+-/
 
+#print Path.Homotopy.transAssocReparamAux_one /-
 theorem transAssocReparamAux_one : transAssocReparamAux 1 = 1 := by
   norm_num [trans_assoc_reparam_aux]
 #align path.homotopy.trans_assoc_reparam_aux_one Path.Homotopy.transAssocReparamAux_one
+-/
 
 #print Path.Homotopy.trans_assoc_reparam /-
 theorem trans_assoc_reparam {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q : Path x₁ x₂) (r : Path x₂ x₃) :
@@ -384,40 +394,45 @@ def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd
 #align fundamental_groupoid.fundamental_groupoid_functor FundamentalGroupoid.fundamentalGroupoidFunctor
 -/
 
--- mathport name: fundamental_groupoid_functor
 scoped notation "π" => FundamentalGroupoid.fundamentalGroupoidFunctor
 
--- mathport name: fundamental_groupoid_functor.obj
 scoped notation "πₓ" => FundamentalGroupoid.fundamentalGroupoidFunctor.obj
 
--- mathport name: fundamental_groupoid_functor.map
 scoped notation "πₘ" => FundamentalGroupoid.fundamentalGroupoidFunctor.map
 
+#print FundamentalGroupoid.map_eq /-
 theorem map_eq {X Y : TopCat} {x₀ x₁ : X} (f : C(X, Y)) (p : Path.Homotopic.Quotient x₀ x₁) :
     (πₘ f).map p = p.mapFn f :=
   rfl
 #align fundamental_groupoid.map_eq FundamentalGroupoid.map_eq
+-/
 
+#print FundamentalGroupoid.toTop /-
 /-- Help the typechecker by converting a point in a groupoid back to a point in
 the underlying topological space. -/
 @[reducible]
 def toTop {X : TopCat} (x : πₓ X) : X :=
   x
 #align fundamental_groupoid.to_top FundamentalGroupoid.toTop
+-/
 
+#print FundamentalGroupoid.fromTop /-
 /-- Help the typechecker by converting a point in a topological space to a
 point in the fundamental groupoid of that space -/
 @[reducible]
 def fromTop {X : TopCat} (x : X) : πₓ X :=
   x
 #align fundamental_groupoid.from_top FundamentalGroupoid.fromTop
+-/
 
+#print FundamentalGroupoid.toPath /-
 /-- Help the typechecker by converting an arrow in the fundamental groupoid of
 a topological space back to a path in that space (i.e., `path.homotopic.quotient`). -/
 @[reducible]
 def toPath {X : TopCat} {x₀ x₁ : πₓ X} (p : x₀ ⟶ x₁) : Path.Homotopic.Quotient x₀ x₁ :=
   p
 #align fundamental_groupoid.to_path FundamentalGroupoid.toPath
+-/
 
 #print FundamentalGroupoid.fromPath /-
 /-- Help the typechecker by convering a path in a topological space to an arrow in the

50251fd6

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -116,7 +116,7 @@ def reflTransSymm (p : Path x₀ x₁) : Homotopy (Path.refl x₀) (p.trans p.sy
   prop' t x hx := by
     cases hx
     · rw [hx]; simp [refl_trans_symm_aux]
-    · rw [Set.mem_singleton_iff] at hx
+    · rw [Set.mem_singleton_iff] at hx 
       rw [hx]
       norm_num [refl_trans_symm_aux]
 #align path.homotopy.refl_trans_symm Path.Homotopy.reflTransSymm
@@ -146,7 +146,7 @@ def transReflReparamAux (t : I) : ℝ :=
 theorem continuous_transReflReparamAux : Continuous transReflReparamAux :=
   by
   refine' continuous_if_le _ _ (Continuous.continuousOn _) (Continuous.continuousOn _) _ <;>
-    [continuity;continuity;continuity;continuity;skip]
+    [continuity; continuity; continuity; continuity; skip]
   intro x hx
   norm_num [hx]
 #align path.homotopy.continuous_trans_refl_reparam_aux Path.Homotopy.continuous_transReflReparamAux
@@ -219,7 +219,8 @@ theorem continuous_transAssocReparamAux : Continuous transAssocReparamAux := by
           (continuous_if_le _ _ (Continuous.continuousOn _) (Continuous.continuousOn _)
               _).ContinuousOn
           _ <;>
-      [continuity;continuity;continuity;continuity;continuity;continuity;continuity;skip;skip] <;>
+      [continuity; continuity; continuity; continuity; continuity; continuity; continuity; skip;
+      skip] <;>
     · intro x hx
       norm_num [hx]
 #align path.homotopy.continuous_trans_assoc_reparam_aux Path.Homotopy.continuous_transAssocReparamAux
@@ -267,7 +268,7 @@ theorem trans_assoc_reparam {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q :
   · have h : ¬(1 / 2 : ℝ) * (x + 1) ≤ 1 / 2 := by linarith
     have h' : ¬2 * ((1 / 2 : ℝ) * (x + 1)) - 1 ≤ 1 / 2 := by linarith
     simp only [h₁, h₅, h, h', if_false, dif_neg (show ¬False from id)]
-    congr ; ring
+    congr; ring
 #align path.homotopy.trans_assoc_reparam Path.Homotopy.trans_assoc_reparam
 -/

50251fd6

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -34,7 +34,7 @@ variable {x₀ x₁ : X}
 
 noncomputable section
 
-open unitInterval
+open scoped unitInterval
 
 namespace Path

50251fd6

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -49,12 +49,6 @@ def reflTransSymmAux (x : I × I) : ℝ :=
 #align path.homotopy.refl_trans_symm_aux Path.Homotopy.reflTransSymmAux
 -/
 
-/- warning: path.homotopy.continuous_refl_trans_symm_aux -> Path.Homotopy.continuous_reflTransSymmAux is a dubious translation:
-lean 3 declaration is
-  Continuous.{0, 0} (Prod.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) Real (Prod.topologicalSpace.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Path.Homotopy.reflTransSymmAux
-but is expected to have type
-  Continuous.{0, 0} (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) Real (instTopologicalSpaceProd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Path.Homotopy.reflTransSymmAux
-Case conversion may be inaccurate. Consider using '#align path.homotopy.continuous_refl_trans_symm_aux Path.Homotopy.continuous_reflTransSymmAuxₓ'. -/
 @[continuity]
 theorem continuous_reflTransSymmAux : Continuous reflTransSymmAux :=
   by
@@ -166,21 +160,9 @@ theorem transReflReparamAux_mem_I (t : I) : transReflReparamAux t ∈ I :=
 #align path.homotopy.trans_refl_reparam_aux_mem_I Path.Homotopy.transReflReparamAux_mem_I
 -/
 
-/- warning: path.homotopy.trans_refl_reparam_aux_zero -> Path.Homotopy.transReflReparamAux_zero is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Path.Homotopy.transReflReparamAux (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (Zero.zero.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
-  Eq.{1} Real (Path.Homotopy.transReflReparamAux (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_refl_reparam_aux_zero Path.Homotopy.transReflReparamAux_zeroₓ'. -/
 theorem transReflReparamAux_zero : transReflReparamAux 0 = 0 := by norm_num [trans_refl_reparam_aux]
 #align path.homotopy.trans_refl_reparam_aux_zero Path.Homotopy.transReflReparamAux_zero
 
-/- warning: path.homotopy.trans_refl_reparam_aux_one -> Path.Homotopy.transReflReparamAux_one is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Path.Homotopy.transReflReparamAux (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (One.one.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
-but is expected to have type
-  Eq.{1} Real (Path.Homotopy.transReflReparamAux (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
-Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_refl_reparam_aux_one Path.Homotopy.transReflReparamAux_oneₓ'. -/
 theorem transReflReparamAux_one : transReflReparamAux 1 = 1 := by norm_num [trans_refl_reparam_aux]
 #align path.homotopy.trans_refl_reparam_aux_one Path.Homotopy.transReflReparamAux_one
 
@@ -251,22 +233,10 @@ theorem transAssocReparamAux_mem_I (t : I) : transAssocReparamAux t ∈ I :=
 #align path.homotopy.trans_assoc_reparam_aux_mem_I Path.Homotopy.transAssocReparamAux_mem_I
 -/
 
-/- warning: path.homotopy.trans_assoc_reparam_aux_zero -> Path.Homotopy.transAssocReparamAux_zero is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Path.Homotopy.transAssocReparamAux (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (Zero.zero.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
-  Eq.{1} Real (Path.Homotopy.transAssocReparamAux (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_assoc_reparam_aux_zero Path.Homotopy.transAssocReparamAux_zeroₓ'. -/
 theorem transAssocReparamAux_zero : transAssocReparamAux 0 = 0 := by
   norm_num [trans_assoc_reparam_aux]
 #align path.homotopy.trans_assoc_reparam_aux_zero Path.Homotopy.transAssocReparamAux_zero
 
-/- warning: path.homotopy.trans_assoc_reparam_aux_one -> Path.Homotopy.transAssocReparamAux_one is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Path.Homotopy.transAssocReparamAux (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (One.one.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
-but is expected to have type
-  Eq.{1} Real (Path.Homotopy.transAssocReparamAux (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
-Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_assoc_reparam_aux_one Path.Homotopy.transAssocReparamAux_oneₓ'. -/
 theorem transAssocReparamAux_one : transAssocReparamAux 1 = 1 := by
   norm_num [trans_assoc_reparam_aux]
 #align path.homotopy.trans_assoc_reparam_aux_one Path.Homotopy.transAssocReparamAux_one
@@ -422,20 +392,11 @@ scoped notation "πₓ" => FundamentalGroupoid.fundamentalGroupoidFunctor.obj
 -- mathport name: fundamental_groupoid_functor.map
 scoped notation "πₘ" => FundamentalGroupoid.fundamentalGroupoidFunctor.map
 
-/- warning: fundamental_groupoid.map_eq -> FundamentalGroupoid.map_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fundamental_groupoid.map_eq FundamentalGroupoid.map_eqₓ'. -/
 theorem map_eq {X Y : TopCat} {x₀ x₁ : X} (f : C(X, Y)) (p : Path.Homotopic.Quotient x₀ x₁) :
     (πₘ f).map p = p.mapFn f :=
   rfl
 #align fundamental_groupoid.map_eq FundamentalGroupoid.map_eq
 
-/- warning: fundamental_groupoid.to_top -> FundamentalGroupoid.toTop is a dubious translation:
-lean 3 declaration is
-  forall {X : TopCat.{u1}}, (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) -> (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X)
-but is expected to have type
-  forall {X : TopCat.{u1}}, (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) -> (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)
-Case conversion may be inaccurate. Consider using '#align fundamental_groupoid.to_top FundamentalGroupoid.toTopₓ'. -/
 /-- Help the typechecker by converting a point in a groupoid back to a point in
 the underlying topological space. -/
 @[reducible]
@@ -443,12 +404,6 @@ def toTop {X : TopCat} (x : πₓ X) : X :=
   x
 #align fundamental_groupoid.to_top FundamentalGroupoid.toTop
 
-/- warning: fundamental_groupoid.from_top -> FundamentalGroupoid.fromTop is a dubious translation:
-lean 3 declaration is
-  forall {X : TopCat.{u1}}, (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) -> (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X))
-but is expected to have type
-  forall {X : TopCat.{u1}}, (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))
-Case conversion may be inaccurate. Consider using '#align fundamental_groupoid.from_top FundamentalGroupoid.fromTopₓ'. -/
 /-- Help the typechecker by converting a point in a topological space to a
 point in the fundamental groupoid of that space -/
 @[reducible]
@@ -456,12 +411,6 @@ def fromTop {X : TopCat} (x : X) : πₓ X :=
   x
 #align fundamental_groupoid.from_top FundamentalGroupoid.fromTop
 
-/- warning: fundamental_groupoid.to_path -> FundamentalGroupoid.toPath is a dubious translation:
-lean 3 declaration is
-  forall {X : TopCat.{u1}} {x₀ : coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)} {x₁ : coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)}, (Quiver.Hom.{succ u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X))))) x₀ x₁) -> (Path.Homotopic.Quotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (TopCat.topologicalSpace.{u1} X) x₀ x₁)
-but is expected to have type
-  forall {X : TopCat.{u1}} {x₀ : CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)} {x₁ : CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)}, (Quiver.Hom.{succ u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))))) x₀ x₁) -> (Path.Homotopic.Quotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) x₀ x₁)
-Case conversion may be inaccurate. Consider using '#align fundamental_groupoid.to_path FundamentalGroupoid.toPathₓ'. -/
 /-- Help the typechecker by converting an arrow in the fundamental groupoid of
 a topological space back to a path in that space (i.e., `path.homotopic.quotient`). -/
 @[reducible]

50251fd6

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -121,8 +121,7 @@ def reflTransSymm (p : Path x₀ x₁) : Homotopy (Path.refl x₀) (p.trans p.sy
         exact ⟨(not_le.1 h).le, unitInterval.le_one x⟩
   prop' t x hx := by
     cases hx
-    · rw [hx]
-      simp [refl_trans_symm_aux]
+    · rw [hx]; simp [refl_trans_symm_aux]
     · rw [Set.mem_singleton_iff] at hx
       rw [hx]
       norm_num [refl_trans_symm_aux]
@@ -286,10 +285,8 @@ theorem trans_assoc_reparam {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q :
   -- TODO: why does split_ifs not reduce the ifs??????
   split_ifs with h₁ h₂ h₃ h₄ h₅
   · simp [h₂, h₃, -one_div]
-  · exfalso
-    linarith
-  · exfalso
-    linarith
+  · exfalso; linarith
+  · exfalso; linarith
   · have h : ¬(x : ℝ) + 1 / 4 ≤ 1 / 2 := by linarith
     have h' : 2 * ((x : ℝ) + 1 / 4) - 1 ≤ 1 / 2 := by linarith
     have h'' : 2 * (2 * (x : ℝ)) - 1 = 2 * (2 * (↑x + 1 / 4) - 1) := by linarith
@@ -300,8 +297,7 @@ theorem trans_assoc_reparam {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q :
   · have h : ¬(1 / 2 : ℝ) * (x + 1) ≤ 1 / 2 := by linarith
     have h' : ¬2 * ((1 / 2 : ℝ) * (x + 1)) - 1 ≤ 1 / 2 := by linarith
     simp only [h₁, h₅, h, h', if_false, dif_neg (show ¬False from id)]
-    congr
-    ring
+    congr ; ring
 #align path.homotopy.trans_assoc_reparam Path.Homotopy.trans_assoc_reparam
 -/

50251fd6

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -427,10 +427,7 @@ scoped notation "πₓ" => FundamentalGroupoid.fundamentalGroupoidFunctor.obj
 scoped notation "πₘ" => FundamentalGroupoid.fundamentalGroupoidFunctor.map
 
 /- warning: fundamental_groupoid.map_eq -> FundamentalGroupoid.map_eq is a dubious translation:
-lean 3 declaration is
-  forall {X : TopCat.{u1}} {Y : TopCat.{u1}} {x₀ : coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X} {x₁ : coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X} (f : ContinuousMap.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} X) (TopCat.topologicalSpace.{u1} Y)) (p : Path.Homotopic.Quotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) x₀ x₁), Eq.{succ u1} (Quiver.Hom.{succ u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X))) (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y))) (CategoryTheory.Functor.map.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X Y f) x₀) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X))) (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y))) (CategoryTheory.Functor.map.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X Y f) x₁)) (CategoryTheory.Functor.map.{u1, u1, u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X))) (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y))) (CategoryTheory.Functor.map.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X Y f) x₀ x₁ p) (Path.Homotopic.Quotient.mapFn.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (FundamentalGroupoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y)) (TopCat.topologicalSpace.{u1} X) (TopCat.topologicalSpace.{u1} Y) x₀ x₁ p f)
-but is expected to have type
-  forall {X : TopCat.{u1}} {Y : TopCat.{u1}} {x₀ : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X} {x₁ : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X} (f : ContinuousMap.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} X) (TopCat.topologicalSpace_coe.{u1} Y)) (p : Path.Homotopic.Quotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) x₀ x₁), Eq.{succ u1} (Quiver.Hom.{succ u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X Y f)) x₀) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X Y f)) x₁)) (Prefunctor.map.{succ u1, succ u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X Y f)) x₀ x₁ p) (Path.Homotopic.Quotient.mapFn.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} X) (TopCat.topologicalSpace_coe.{u1} Y) x₀ x₁ p f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align fundamental_groupoid.map_eq FundamentalGroupoid.map_eqₓ'. -/
 theorem map_eq {X Y : TopCat} {x₀ x₁ : X} (f : C(X, Y)) (p : Path.Homotopic.Quotient x₀ x₁) :
     (πₘ f).map p = p.mapFn f :=

50251fd6

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -153,7 +153,7 @@ def transReflReparamAux (t : I) : ℝ :=
 theorem continuous_transReflReparamAux : Continuous transReflReparamAux :=
   by
   refine' continuous_if_le _ _ (Continuous.continuousOn _) (Continuous.continuousOn _) _ <;>
-    [continuity, continuity, continuity, continuity, skip]
+    [continuity;continuity;continuity;continuity;skip]
   intro x hx
   norm_num [hx]
 #align path.homotopy.continuous_trans_refl_reparam_aux Path.Homotopy.continuous_transReflReparamAux
@@ -238,8 +238,7 @@ theorem continuous_transAssocReparamAux : Continuous transAssocReparamAux := by
           (continuous_if_le _ _ (Continuous.continuousOn _) (Continuous.continuousOn _)
               _).ContinuousOn
           _ <;>
-      [continuity, continuity, continuity, continuity, continuity, continuity, continuity, skip,
-      skip] <;>
+      [continuity;continuity;continuity;continuity;continuity;continuity;continuity;skip;skip] <;>
     · intro x hx
       norm_num [hx]
 #align path.homotopy.continuous_trans_assoc_reparam_aux Path.Homotopy.continuous_transAssocReparamAux

50251fd6

bump to nightly-2023-05-19-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

9a2fedb8

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
 
 ! This file was ported from Lean 3 source module algebraic_topology.fundamental_groupoid.basic
-! leanprover-community/mathlib commit 3d7987cda72abc473c7cdbbb075170e9ac620042
+! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Homotopy.Path
 /-!
 # Fundamental groupoid of a space
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a topological space `X`, we can define the fundamental groupoid of `X` to be the category with
 objects being points of `X`, and morphisms `x ⟶ y` being paths from `x` to `y`, quotiented by
 homotopy equivalence. With this, the fundamental group of `X` based at `x` is just the automorphism

3d7987cd

bump to nightly-2023-05-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/f8c79b0a623404854a2902b836eac32156fd7712

311ac93c

Diff

@@ -39,11 +39,19 @@ namespace Homotopy
 
 section
 
+#print Path.Homotopy.reflTransSymmAux /-
 /-- Auxilliary function for `refl_trans_symm` -/
 def reflTransSymmAux (x : I × I) : ℝ :=
   if (x.2 : ℝ) ≤ 1 / 2 then x.1 * 2 * x.2 else x.1 * (2 - 2 * x.2)
 #align path.homotopy.refl_trans_symm_aux Path.Homotopy.reflTransSymmAux
+-/
 
+/- warning: path.homotopy.continuous_refl_trans_symm_aux -> Path.Homotopy.continuous_reflTransSymmAux is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} (Prod.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) Real (Prod.topologicalSpace.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Path.Homotopy.reflTransSymmAux
+but is expected to have type
+  Continuous.{0, 0} (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) Real (instTopologicalSpaceProd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Path.Homotopy.reflTransSymmAux
+Case conversion may be inaccurate. Consider using '#align path.homotopy.continuous_refl_trans_symm_aux Path.Homotopy.continuous_reflTransSymmAuxₓ'. -/
 @[continuity]
 theorem continuous_reflTransSymmAux : Continuous reflTransSymmAux :=
   by
@@ -56,6 +64,7 @@ theorem continuous_reflTransSymmAux : Continuous reflTransSymmAux :=
   norm_num [hx, mul_assoc]
 #align path.homotopy.continuous_refl_trans_symm_aux Path.Homotopy.continuous_reflTransSymmAux
 
+#print Path.Homotopy.reflTransSymmAux_mem_I /-
 theorem reflTransSymmAux_mem_I (x : I × I) : reflTransSymmAux x ∈ I :=
   by
   dsimp only [refl_trans_symm_aux]
@@ -82,7 +91,9 @@ theorem reflTransSymmAux_mem_I (x : I × I) : reflTransSymmAux x ∈ I :=
       · linarith [unitInterval.nonneg x.2, unitInterval.le_one x.2]
       · linarith [unitInterval.nonneg x.2, unitInterval.le_one x.2]
 #align path.homotopy.refl_trans_symm_aux_mem_I Path.Homotopy.reflTransSymmAux_mem_I
+-/
 
+#print Path.Homotopy.reflTransSymm /-
 /-- For any path `p` from `x₀` to `x₁`, we have a homotopy from the constant path based at `x₀` to
   `p.trans p.symm`. -/
 def reflTransSymm (p : Path x₀ x₁) : Homotopy (Path.refl x₀) (p.trans p.symm)
@@ -113,22 +124,28 @@ def reflTransSymm (p : Path x₀ x₁) : Homotopy (Path.refl x₀) (p.trans p.sy
       rw [hx]
       norm_num [refl_trans_symm_aux]
 #align path.homotopy.refl_trans_symm Path.Homotopy.reflTransSymm
+-/
 
+#print Path.Homotopy.reflSymmTrans /-
 /-- For any path `p` from `x₀` to `x₁`, we have a homotopy from the constant path based at `x₁` to
   `p.symm.trans p`. -/
 def reflSymmTrans (p : Path x₀ x₁) : Homotopy (Path.refl x₁) (p.symm.trans p) :=
   (reflTransSymm p.symm).cast rfl <| congr_arg _ Path.symm_symm
 #align path.homotopy.refl_symm_trans Path.Homotopy.reflSymmTrans
+-/
 
 end
 
 section TransRefl
 
+#print Path.Homotopy.transReflReparamAux /-
 /-- Auxilliary function for `trans_refl_reparam` -/
 def transReflReparamAux (t : I) : ℝ :=
   if (t : ℝ) ≤ 1 / 2 then 2 * t else 1
 #align path.homotopy.trans_refl_reparam_aux Path.Homotopy.transReflReparamAux
+-/
 
+#print Path.Homotopy.continuous_transReflReparamAux /-
 @[continuity]
 theorem continuous_transReflReparamAux : Continuous transReflReparamAux :=
   by
@@ -137,19 +154,35 @@ theorem continuous_transReflReparamAux : Continuous transReflReparamAux :=
   intro x hx
   norm_num [hx]
 #align path.homotopy.continuous_trans_refl_reparam_aux Path.Homotopy.continuous_transReflReparamAux
+-/
 
+#print Path.Homotopy.transReflReparamAux_mem_I /-
 theorem transReflReparamAux_mem_I (t : I) : transReflReparamAux t ∈ I :=
   by
   unfold trans_refl_reparam_aux
   split_ifs <;> constructor <;> linarith [unitInterval.le_one t, unitInterval.nonneg t]
 #align path.homotopy.trans_refl_reparam_aux_mem_I Path.Homotopy.transReflReparamAux_mem_I
+-/
 
+/- warning: path.homotopy.trans_refl_reparam_aux_zero -> Path.Homotopy.transReflReparamAux_zero is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Path.Homotopy.transReflReparamAux (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (Zero.zero.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  Eq.{1} Real (Path.Homotopy.transReflReparamAux (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_refl_reparam_aux_zero Path.Homotopy.transReflReparamAux_zeroₓ'. -/
 theorem transReflReparamAux_zero : transReflReparamAux 0 = 0 := by norm_num [trans_refl_reparam_aux]
 #align path.homotopy.trans_refl_reparam_aux_zero Path.Homotopy.transReflReparamAux_zero
 
+/- warning: path.homotopy.trans_refl_reparam_aux_one -> Path.Homotopy.transReflReparamAux_one is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Path.Homotopy.transReflReparamAux (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (One.one.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  Eq.{1} Real (Path.Homotopy.transReflReparamAux (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_refl_reparam_aux_one Path.Homotopy.transReflReparamAux_oneₓ'. -/
 theorem transReflReparamAux_one : transReflReparamAux 1 = 1 := by norm_num [trans_refl_reparam_aux]
 #align path.homotopy.trans_refl_reparam_aux_one Path.Homotopy.transReflReparamAux_one
 
+#print Path.Homotopy.trans_refl_reparam /-
 theorem trans_refl_reparam (p : Path x₀ x₁) :
     p.trans (Path.refl x₁) =
       p.reparam (fun t => ⟨transReflReparamAux t, transReflReparamAux_mem_I t⟩) (by continuity)
@@ -162,7 +195,9 @@ theorem trans_refl_reparam (p : Path x₀ x₁) :
   · rfl
   · simp
 #align path.homotopy.trans_refl_reparam Path.Homotopy.trans_refl_reparam
+-/
 
+#print Path.Homotopy.transRefl /-
 /-- For any path `p` from `x₀` to `x₁`, we have a homotopy from `p.trans (path.refl x₁)` to `p`.
 -/
 def transRefl (p : Path x₀ x₁) : Homotopy (p.trans (Path.refl x₁)) p :=
@@ -171,22 +206,28 @@ def transRefl (p : Path x₀ x₁) : Homotopy (p.trans (Path.refl x₁)) p :=
           (Subtype.ext transReflReparamAux_one)).cast
       rfl (trans_refl_reparam p).symm).symm
 #align path.homotopy.trans_refl Path.Homotopy.transRefl
+-/
 
+#print Path.Homotopy.reflTrans /-
 /-- For any path `p` from `x₀` to `x₁`, we have a homotopy from `(path.refl x₀).trans p` to `p`.
 -/
 def reflTrans (p : Path x₀ x₁) : Homotopy ((Path.refl x₀).trans p) p :=
   (transRefl p.symm).symm₂.cast (by simp) (by simp)
 #align path.homotopy.refl_trans Path.Homotopy.reflTrans
+-/
 
 end TransRefl
 
 section Assoc
 
+#print Path.Homotopy.transAssocReparamAux /-
 /-- Auxilliary function for `trans_assoc_reparam`. -/
 def transAssocReparamAux (t : I) : ℝ :=
   if (t : ℝ) ≤ 1 / 4 then 2 * t else if (t : ℝ) ≤ 1 / 2 then t + 1 / 4 else 1 / 2 * (t + 1)
 #align path.homotopy.trans_assoc_reparam_aux Path.Homotopy.transAssocReparamAux
+-/
 
+#print Path.Homotopy.continuous_transAssocReparamAux /-
 @[continuity]
 theorem continuous_transAssocReparamAux : Continuous transAssocReparamAux := by
   refine'
@@ -199,21 +240,37 @@ theorem continuous_transAssocReparamAux : Continuous transAssocReparamAux := by
     · intro x hx
       norm_num [hx]
 #align path.homotopy.continuous_trans_assoc_reparam_aux Path.Homotopy.continuous_transAssocReparamAux
+-/
 
+#print Path.Homotopy.transAssocReparamAux_mem_I /-
 theorem transAssocReparamAux_mem_I (t : I) : transAssocReparamAux t ∈ I :=
   by
   unfold trans_assoc_reparam_aux
   split_ifs <;> constructor <;> linarith [unitInterval.le_one t, unitInterval.nonneg t]
 #align path.homotopy.trans_assoc_reparam_aux_mem_I Path.Homotopy.transAssocReparamAux_mem_I
+-/
 
+/- warning: path.homotopy.trans_assoc_reparam_aux_zero -> Path.Homotopy.transAssocReparamAux_zero is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Path.Homotopy.transAssocReparamAux (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (Zero.zero.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  Eq.{1} Real (Path.Homotopy.transAssocReparamAux (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_assoc_reparam_aux_zero Path.Homotopy.transAssocReparamAux_zeroₓ'. -/
 theorem transAssocReparamAux_zero : transAssocReparamAux 0 = 0 := by
   norm_num [trans_assoc_reparam_aux]
 #align path.homotopy.trans_assoc_reparam_aux_zero Path.Homotopy.transAssocReparamAux_zero
 
+/- warning: path.homotopy.trans_assoc_reparam_aux_one -> Path.Homotopy.transAssocReparamAux_one is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Path.Homotopy.transAssocReparamAux (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (One.one.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  Eq.{1} Real (Path.Homotopy.transAssocReparamAux (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_assoc_reparam_aux_one Path.Homotopy.transAssocReparamAux_oneₓ'. -/
 theorem transAssocReparamAux_one : transAssocReparamAux 1 = 1 := by
   norm_num [trans_assoc_reparam_aux]
 #align path.homotopy.trans_assoc_reparam_aux_one Path.Homotopy.transAssocReparamAux_one
 
+#print Path.Homotopy.trans_assoc_reparam /-
 theorem trans_assoc_reparam {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q : Path x₁ x₂) (r : Path x₂ x₃) :
     (p.trans q).trans r =
       (p.trans (q.trans r)).reparam
@@ -244,7 +301,9 @@ theorem trans_assoc_reparam {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q :
     congr
     ring
 #align path.homotopy.trans_assoc_reparam Path.Homotopy.trans_assoc_reparam
+-/
 
+#print Path.Homotopy.transAssoc /-
 /-- For paths `p q r`, we have a homotopy from `(p.trans q).trans r` to `p.trans (q.trans r)`.
 -/
 def transAssoc {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q : Path x₁ x₂) (r : Path x₂ x₃) :
@@ -254,6 +313,7 @@ def transAssoc {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q : Path x₁ x
           (Subtype.ext transAssocReparamAux_zero) (Subtype.ext transAssocReparamAux_one)).cast
       rfl (trans_assoc_reparam p q r).symm).symm
 #align path.homotopy.trans_assoc Path.Homotopy.transAssoc
+-/
 
 end Assoc
 
@@ -261,6 +321,7 @@ end Homotopy
 
 end Path
 
+#print FundamentalGroupoid /-
 /--
 The fundamental groupoid of a space `X` is defined to be a type synonym for `X`, and we subsequently
 put a `category_theory.groupoid` structure on it.
@@ -268,6 +329,7 @@ put a `category_theory.groupoid` structure on it.
 def FundamentalGroupoid (X : Type u) :=
   X
 #align fundamental_groupoid FundamentalGroupoid
+-/
 
 namespace FundamentalGroupoid
 
@@ -309,14 +371,19 @@ instance : CategoryTheory.Groupoid (FundamentalGroupoid X)
       show ⟦a.trans a.symm⟧ = ⟦Path.refl x⟧ from
         Quotient.sound ⟨(Path.Homotopy.reflTransSymm a).symm⟩
 
+#print FundamentalGroupoid.comp_eq /-
 theorem comp_eq (x y z : FundamentalGroupoid X) (p : x ⟶ y) (q : y ⟶ z) : p ≫ q = p.comp q :=
   rfl
 #align fundamental_groupoid.comp_eq FundamentalGroupoid.comp_eq
+-/
 
+#print FundamentalGroupoid.id_eq_path_refl /-
 theorem id_eq_path_refl (x : FundamentalGroupoid X) : 𝟙 x = ⟦Path.refl x⟧ :=
   rfl
 #align fundamental_groupoid.id_eq_path_refl FundamentalGroupoid.id_eq_path_refl
+-/
 
+#print FundamentalGroupoid.fundamentalGroupoidFunctor /-
 /-- The functor sending a topological space `X` to its fundamental groupoid.
 -/
 def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd
@@ -346,6 +413,7 @@ def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd
     simp only [Quotient.map_mk, Path.map_map, Quotient.eq']
     rfl
 #align fundamental_groupoid.fundamental_groupoid_functor FundamentalGroupoid.fundamentalGroupoidFunctor
+-/
 
 -- mathport name: fundamental_groupoid_functor
 scoped notation "π" => FundamentalGroupoid.fundamentalGroupoidFunctor
@@ -356,11 +424,23 @@ scoped notation "πₓ" => FundamentalGroupoid.fundamentalGroupoidFunctor.obj
 -- mathport name: fundamental_groupoid_functor.map
 scoped notation "πₘ" => FundamentalGroupoid.fundamentalGroupoidFunctor.map
 
+/- warning: fundamental_groupoid.map_eq -> FundamentalGroupoid.map_eq is a dubious translation:
+lean 3 declaration is
+  forall {X : TopCat.{u1}} {Y : TopCat.{u1}} {x₀ : coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X} {x₁ : coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X} (f : ContinuousMap.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} X) (TopCat.topologicalSpace.{u1} Y)) (p : Path.Homotopic.Quotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) x₀ x₁), Eq.{succ u1} (Quiver.Hom.{succ u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X))) (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y))) (CategoryTheory.Functor.map.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X Y f) x₀) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X))) (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y))) (CategoryTheory.Functor.map.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X Y f) x₁)) (CategoryTheory.Functor.map.{u1, u1, u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X))) (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} Y))) (CategoryTheory.Functor.map.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X Y f) x₀ x₁ p) (Path.Homotopic.Quotient.mapFn.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (FundamentalGroupoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y)) (TopCat.topologicalSpace.{u1} X) (TopCat.topologicalSpace.{u1} Y) x₀ x₁ p f)
+but is expected to have type
+  forall {X : TopCat.{u1}} {Y : TopCat.{u1}} {x₀ : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X} {x₁ : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X} (f : ContinuousMap.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} X) (TopCat.topologicalSpace_coe.{u1} Y)) (p : Path.Homotopic.Quotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) x₀ x₁), Eq.{succ u1} (Quiver.Hom.{succ u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X Y f)) x₀) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X Y f)) x₁)) (Prefunctor.map.{succ u1, succ u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))) (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) Y))) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X Y f)) x₀ x₁ p) (Path.Homotopic.Quotient.mapFn.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} X) (TopCat.topologicalSpace_coe.{u1} Y) x₀ x₁ p f)
+Case conversion may be inaccurate. Consider using '#align fundamental_groupoid.map_eq FundamentalGroupoid.map_eqₓ'. -/
 theorem map_eq {X Y : TopCat} {x₀ x₁ : X} (f : C(X, Y)) (p : Path.Homotopic.Quotient x₀ x₁) :
     (πₘ f).map p = p.mapFn f :=
   rfl
 #align fundamental_groupoid.map_eq FundamentalGroupoid.map_eq
 
+/- warning: fundamental_groupoid.to_top -> FundamentalGroupoid.toTop is a dubious translation:
+lean 3 declaration is
+  forall {X : TopCat.{u1}}, (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) -> (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X)
+but is expected to have type
+  forall {X : TopCat.{u1}}, (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) -> (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)
+Case conversion may be inaccurate. Consider using '#align fundamental_groupoid.to_top FundamentalGroupoid.toTopₓ'. -/
 /-- Help the typechecker by converting a point in a groupoid back to a point in
 the underlying topological space. -/
 @[reducible]
@@ -368,6 +448,12 @@ def toTop {X : TopCat} (x : πₓ X) : X :=
   x
 #align fundamental_groupoid.to_top FundamentalGroupoid.toTop
 
+/- warning: fundamental_groupoid.from_top -> FundamentalGroupoid.fromTop is a dubious translation:
+lean 3 declaration is
+  forall {X : TopCat.{u1}}, (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) -> (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X))
+but is expected to have type
+  forall {X : TopCat.{u1}}, (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))
+Case conversion may be inaccurate. Consider using '#align fundamental_groupoid.from_top FundamentalGroupoid.fromTopₓ'. -/
 /-- Help the typechecker by converting a point in a topological space to a
 point in the fundamental groupoid of that space -/
 @[reducible]
@@ -375,6 +461,12 @@ def fromTop {X : TopCat} (x : X) : πₓ X :=
   x
 #align fundamental_groupoid.from_top FundamentalGroupoid.fromTop
 
+/- warning: fundamental_groupoid.to_path -> FundamentalGroupoid.toPath is a dubious translation:
+lean 3 declaration is
+  forall {X : TopCat.{u1}} {x₀ : coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)} {x₁ : coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)}, (Quiver.Hom.{succ u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (CategoryTheory.Grpd.str'.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X))))) x₀ x₁) -> (Path.Homotopic.Quotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CategoryTheory.Grpd.{u1, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1} X)) (TopCat.topologicalSpace.{u1} X) x₀ x₁)
+but is expected to have type
+  forall {X : TopCat.{u1}} {x₀ : CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)} {x₁ : CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)}, (Quiver.Hom.{succ u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Groupoid.toCategory.{u1, u1} (CategoryTheory.Bundled.α.{u1, succ u1} CategoryTheory.Groupoid.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X)) (CategoryTheory.Grpd.str'.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) CategoryTheory.Grpd.{u1, u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} CategoryTheory.Grpd.{u1, u1} CategoryTheory.Grpd.category.{u1, u1} FundamentalGroupoid.fundamentalGroupoidFunctor.{u1}) X))))) x₀ x₁) -> (Path.Homotopic.Quotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) x₀ x₁)
+Case conversion may be inaccurate. Consider using '#align fundamental_groupoid.to_path FundamentalGroupoid.toPathₓ'. -/
 /-- Help the typechecker by converting an arrow in the fundamental groupoid of
 a topological space back to a path in that space (i.e., `path.homotopic.quotient`). -/
 @[reducible]
@@ -382,12 +474,14 @@ def toPath {X : TopCat} {x₀ x₁ : πₓ X} (p : x₀ ⟶ x₁) : Path.Homotop
   p
 #align fundamental_groupoid.to_path FundamentalGroupoid.toPath
 
+#print FundamentalGroupoid.fromPath /-
 /-- Help the typechecker by convering a path in a topological space to an arrow in the
 fundamental groupoid of that space. -/
 @[reducible]
 def fromPath {X : TopCat} {x₀ x₁ : X} (p : Path.Homotopic.Quotient x₀ x₁) : x₀ ⟶ x₁ :=
   p
 #align fundamental_groupoid.from_path FundamentalGroupoid.fromPath
+-/
 
 end FundamentalGroupoid

3d7987cd

bump to nightly-2023-05-03-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

fde4375d

Diff

@@ -319,7 +319,7 @@ theorem id_eq_path_refl (x : FundamentalGroupoid X) : 𝟙 x = ⟦Path.refl x⟧
 
 /-- The functor sending a topological space `X` to its fundamental groupoid.
 -/
-def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.GroupoidCat
+def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd
     where
   obj X := { α := FundamentalGroupoid X }
   map X Y f :=

3d7987cd

bump to nightly-2023-03-23-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

53b827ba

Diff

@@ -223,7 +223,7 @@ theorem trans_assoc_reparam {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q :
   ext
   simp only [trans_assoc_reparam_aux, Path.trans_apply, mul_inv_cancel_left₀, not_le,
     Function.comp_apply, Ne.def, not_false_iff, bit0_eq_zero, one_ne_zero, mul_ite, Subtype.coe_mk,
-    Path.coe_to_fun]
+    Path.coe_reparam]
   -- TODO: why does split_ifs not reduce the ifs??????
   split_ifs with h₁ h₂ h₃ h₄ h₅
   · simp [h₂, h₃, -one_div]

3d7987cd

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

3d7987cd

chore: split Subsingleton,Nontrivial off of Data.Set.Basic (#11832)

Moves definition of and lemmas related to Set.Subsingleton and Set.Nontrivial to a new file, so that Basic can be shorter.

493a947e

Diff

@@ -7,7 +7,7 @@ import Mathlib.CategoryTheory.Category.Grpd
 import Mathlib.CategoryTheory.Groupoid
 import Mathlib.Topology.Category.TopCat.Basic
 import Mathlib.Topology.Homotopy.Path
-import Mathlib.Data.Set.Basic
+import Mathlib.Data.Set.Subsingleton
 
 #align_import algebraic_topology.fundamental_groupoid.basic from "leanprover-community/mathlib"@"3d7987cda72abc473c7cdbbb075170e9ac620042"

3d7987cd

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -271,7 +271,7 @@ end Path
 subsequently put a `CategoryTheory.Groupoid` structure on it. -/
 @[ext]
 structure FundamentalGroupoid (X : Type u) where
-  /-- View a term of `FundamentalGroupoid X` as a term of `X`.-/
+  /-- View a term of `FundamentalGroupoid X` as a term of `X`. -/
   as : X
 #align fundamental_groupoid FundamentalGroupoid

3d7987cd

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -217,7 +217,7 @@ theorem trans_assoc_reparam {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q :
         (Subtype.ext transAssocReparamAux_zero) (Subtype.ext transAssocReparamAux_one) := by
   ext x
   simp only [transAssocReparamAux, Path.trans_apply, mul_inv_cancel_left₀, not_le,
-    Function.comp_apply, Ne.def, not_false_iff, bit0_eq_zero, one_ne_zero, mul_ite, Subtype.coe_mk,
+    Function.comp_apply, Ne, not_false_iff, bit0_eq_zero, one_ne_zero, mul_ite, Subtype.coe_mk,
     Path.coe_reparam]
   -- TODO: why does split_ifs not reduce the ifs??????
   split_ifs with h₁ h₂ h₃ h₄ h₅

3d7987cd

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -25,7 +25,6 @@ open CategoryTheory
 universe u v
 
 variable {X : Type u} {Y : Type v} [TopologicalSpace X] [TopologicalSpace Y]
-
 variable {x₀ x₁ : X}
 
 noncomputable section

3d7987cd

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -108,6 +108,7 @@ def reflTransSymm (p : Path x₀ x₁) : Homotopy (Path.refl x₀) (p.trans p.sy
     cases hx with
     | inl hx
     | inr hx =>
+      set_option tactic.skipAssignedInstances false in
       rw [hx]
       norm_num [reflTransSymmAux]
 #align path.homotopy.refl_trans_symm Path.Homotopy.reflTransSymm
@@ -142,11 +143,11 @@ set_option linter.uppercaseLean3 false in
 #align path.homotopy.trans_refl_reparam_aux_mem_I Path.Homotopy.transReflReparamAux_mem_I
 
 theorem transReflReparamAux_zero : transReflReparamAux 0 = 0 := by
-  norm_num [transReflReparamAux]
+  set_option tactic.skipAssignedInstances false in norm_num [transReflReparamAux]
 #align path.homotopy.trans_refl_reparam_aux_zero Path.Homotopy.transReflReparamAux_zero
 
 theorem transReflReparamAux_one : transReflReparamAux 1 = 1 := by
-  norm_num [transReflReparamAux]
+  set_option tactic.skipAssignedInstances false in norm_num [transReflReparamAux]
 #align path.homotopy.trans_refl_reparam_aux_one Path.Homotopy.transReflReparamAux_one
 
 theorem trans_refl_reparam (p : Path x₀ x₁) :
@@ -193,7 +194,7 @@ theorem continuous_transAssocReparamAux : Continuous transAssocReparamAux := by
     [continuity; continuity; continuity; continuity; continuity; continuity; continuity; skip;
       skip] <;>
     · intro x hx
-      norm_num [hx]
+      set_option tactic.skipAssignedInstances false in norm_num [hx]
 #align path.homotopy.continuous_trans_assoc_reparam_aux Path.Homotopy.continuous_transAssocReparamAux
 
 theorem transAssocReparamAux_mem_I (t : I) : transAssocReparamAux t ∈ I := by
@@ -203,11 +204,11 @@ set_option linter.uppercaseLean3 false in
 #align path.homotopy.trans_assoc_reparam_aux_mem_I Path.Homotopy.transAssocReparamAux_mem_I
 
 theorem transAssocReparamAux_zero : transAssocReparamAux 0 = 0 := by
-  norm_num [transAssocReparamAux]
+  set_option tactic.skipAssignedInstances false in norm_num [transAssocReparamAux]
 #align path.homotopy.trans_assoc_reparam_aux_zero Path.Homotopy.transAssocReparamAux_zero
 
 theorem transAssocReparamAux_one : transAssocReparamAux 1 = 1 := by
-  norm_num [transAssocReparamAux]
+  set_option tactic.skipAssignedInstances false in norm_num [transAssocReparamAux]
 #align path.homotopy.trans_assoc_reparam_aux_one Path.Homotopy.transAssocReparamAux_one
 
 theorem trans_assoc_reparam {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q : Path x₁ x₂) (r : Path x₂ x₃) :

3d7987cd

chore(*): shake imports (#10199)

Remove Data.Set.Basic from scripts/noshake.json.
Remove an exception that was used by examples only, move these examples to a new test file.
Drop an exception for Order.Filter.Basic dependency on Control.Traversable.Instances, as the relevant parts were moved to Order.Filter.ListTraverse.
Run lake exe shake --fix.

c167d468

Diff

@@ -7,6 +7,7 @@ import Mathlib.CategoryTheory.Category.Grpd
 import Mathlib.CategoryTheory.Groupoid
 import Mathlib.Topology.Category.TopCat.Basic
 import Mathlib.Topology.Homotopy.Path
+import Mathlib.Data.Set.Basic
 
 #align_import algebraic_topology.fundamental_groupoid.basic from "leanprover-community/mathlib"@"3d7987cda72abc473c7cdbbb075170e9ac620042"

3d7987cd

doc: @[inherit_doc] on notations (#9942)

Make all the notations that unambiguously should inherit the docstring of their definition actually inherit it.

Also write a few docstrings by hand. I only wrote the ones I was competent to write and which I was sure of. Some docstrings come from mathlib3 as they were lost during the early port.

This PR is only intended as a first pass There are many more docstrings to add.

08f7e99d

Diff

@@ -387,8 +387,12 @@ def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd where
     rfl
 #align fundamental_groupoid.fundamental_groupoid_functor FundamentalGroupoid.fundamentalGroupoidFunctor
 
-scoped notation "π" => FundamentalGroupoid.fundamentalGroupoidFunctor
+@[inherit_doc] scoped notation "π" => FundamentalGroupoid.fundamentalGroupoidFunctor
+
+/-- The fundamental groupoid of a topological space. -/
 scoped notation "πₓ" => FundamentalGroupoid.fundamentalGroupoidFunctor.obj
+
+/-- The functor between fundamental groupoids induced by a continuous map. -/
 scoped notation "πₘ" => FundamentalGroupoid.fundamentalGroupoidFunctor.map
 
 theorem map_eq {X Y : TopCat} {x₀ x₁ : X} (f : C(X, Y)) (p : Path.Homotopic.Quotient x₀ x₁) :

3d7987cd

feat(/Equiv/): Add symm_bijective lemmas next to symm_symms (#8444)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: lines <34025592+linesthatinterlace@users.noreply.github.com>

e368f2a5

Diff

@@ -114,7 +114,7 @@ def reflTransSymm (p : Path x₀ x₁) : Homotopy (Path.refl x₀) (p.trans p.sy
 /-- For any path `p` from `x₀` to `x₁`, we have a homotopy from the constant path based at `x₁` to
   `p.symm.trans p`. -/
 def reflSymmTrans (p : Path x₀ x₁) : Homotopy (Path.refl x₁) (p.symm.trans p) :=
-  (reflTransSymm p.symm).cast rfl <| congr_arg _ Path.symm_symm
+  (reflTransSymm p.symm).cast rfl <| congr_arg _ (Path.symm_symm _)
 #align path.homotopy.refl_symm_trans Path.Homotopy.reflSymmTrans
 
 end

3d7987cd

fix: Fix FundamentalGroupoid being reducible. (#8257)

Instead it is now the opposite -- a structure with a single field.

zulip discussion

Co-authored-by: Adam Topaz <adamtopaz@users.noreply.github.com>

6b362d1e

Diff

@@ -266,35 +266,77 @@ end Homotopy
 
 end Path
 
-/-- The fundamental groupoid of a space `X` is defined to be a type synonym for `X`, and we
+/-- The fundamental groupoid of a space `X` is defined to be a wrapper around `X`, and we
 subsequently put a `CategoryTheory.Groupoid` structure on it. -/
-def FundamentalGroupoid (X : Type u) := X
+@[ext]
+structure FundamentalGroupoid (X : Type u) where
+  /-- View a term of `FundamentalGroupoid X` as a term of `X`.-/
+  as : X
 #align fundamental_groupoid FundamentalGroupoid
 
 namespace FundamentalGroupoid
 
-instance {X : Type u} [h : Inhabited X] : Inhabited (FundamentalGroupoid X) := h
-
-attribute [reducible] FundamentalGroupoid
+/-- The equivalence between `X` and the underlying type of its fundamental groupoid.
+  This is useful for transferring constructions (instances, etc.)
+  from `X` to `πₓ X`. -/
+@[simps]
+def equiv (X : Type*) : FundamentalGroupoid X ≃ X where
+  toFun x := x.as
+  invFun x := .mk x
+  left_inv _ := rfl
+  right_inv _ := rfl
+
+@[simp]
+lemma isEmpty_iff (X : Type*) :
+    IsEmpty (FundamentalGroupoid X) ↔ IsEmpty X :=
+  equiv _ |>.isEmpty_congr
+
+instance (X : Type*) [IsEmpty X] :
+    IsEmpty (FundamentalGroupoid X) :=
+  equiv _ |>.isEmpty
+
+@[simp]
+lemma nonempty_iff (X : Type*) :
+    Nonempty (FundamentalGroupoid X) ↔ Nonempty X :=
+  equiv _ |>.nonempty_congr
+
+instance (X : Type*) [Nonempty X] :
+    Nonempty (FundamentalGroupoid X) :=
+  equiv _ |>.nonempty
+
+@[simp]
+lemma subsingleton_iff (X : Type*) :
+    Subsingleton (FundamentalGroupoid X) ↔ Subsingleton X :=
+  equiv _ |>.subsingleton_congr
+
+instance (X : Type*) [Subsingleton X] :
+    Subsingleton (FundamentalGroupoid X) :=
+  equiv _ |>.subsingleton
+
+-- TODO: It seems that `Equiv.nontrivial_congr` doesn't exist.
+-- Once it is added, please add the corresponding lemma and instance.
+
+instance {X : Type u} [Inhabited X] : Inhabited (FundamentalGroupoid X) :=
+  ⟨⟨default⟩⟩
 
 attribute [local instance] Path.Homotopic.setoid
 
 instance : CategoryTheory.Groupoid (FundamentalGroupoid X) where
-  Hom x y := Path.Homotopic.Quotient x y
-  id x := ⟦Path.refl x⟧
+  Hom x y := Path.Homotopic.Quotient x.as y.as
+  id x := ⟦Path.refl x.as⟧
   comp {x y z} := Path.Homotopic.Quotient.comp
   id_comp {x y} f :=
     Quotient.inductionOn f fun a =>
-      show ⟦(Path.refl x).trans a⟧ = ⟦a⟧ from Quotient.sound ⟨Path.Homotopy.reflTrans a⟩
+      show ⟦(Path.refl x.as).trans a⟧ = ⟦a⟧ from Quotient.sound ⟨Path.Homotopy.reflTrans a⟩
   comp_id {x y} f :=
     Quotient.inductionOn f fun a =>
-      show ⟦a.trans (Path.refl y)⟧ = ⟦a⟧ from Quotient.sound ⟨Path.Homotopy.transRefl a⟩
+      show ⟦a.trans (Path.refl y.as)⟧ = ⟦a⟧ from Quotient.sound ⟨Path.Homotopy.transRefl a⟩
   assoc {w x y z} f g h :=
     Quotient.inductionOn₃ f g h fun p q r =>
       show ⟦(p.trans q).trans r⟧ = ⟦p.trans (q.trans r)⟧ from
         Quotient.sound ⟨Path.Homotopy.transAssoc p q r⟩
   inv {x y} p :=
-    Quotient.lift (fun l : Path x y => ⟦l.symm⟧)
+    Quotient.lift (fun l : Path x.as y.as => ⟦l.symm⟧)
       (by
         rintro a b ⟨h⟩
         simp only
@@ -303,24 +345,24 @@ instance : CategoryTheory.Groupoid (FundamentalGroupoid X) where
       p
   inv_comp {x y} f :=
     Quotient.inductionOn f fun a =>
-      show ⟦a.symm.trans a⟧ = ⟦Path.refl y⟧ from
+      show ⟦a.symm.trans a⟧ = ⟦Path.refl y.as⟧ from
         Quotient.sound ⟨(Path.Homotopy.reflSymmTrans a).symm⟩
   comp_inv {x y} f :=
     Quotient.inductionOn f fun a =>
-      show ⟦a.trans a.symm⟧ = ⟦Path.refl x⟧ from
+      show ⟦a.trans a.symm⟧ = ⟦Path.refl x.as⟧ from
         Quotient.sound ⟨(Path.Homotopy.reflTransSymm a).symm⟩
 
 theorem comp_eq (x y z : FundamentalGroupoid X) (p : x ⟶ y) (q : y ⟶ z) : p ≫ q = p.comp q := rfl
 #align fundamental_groupoid.comp_eq FundamentalGroupoid.comp_eq
 
-theorem id_eq_path_refl (x : FundamentalGroupoid X) : 𝟙 x = ⟦Path.refl x⟧ := rfl
+theorem id_eq_path_refl (x : FundamentalGroupoid X) : 𝟙 x = ⟦Path.refl x.as⟧ := rfl
 #align fundamental_groupoid.id_eq_path_refl FundamentalGroupoid.id_eq_path_refl
 
 /-- The functor sending a topological space `X` to its fundamental groupoid. -/
 def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd where
   obj X := { α := FundamentalGroupoid X }
   map f :=
-    { obj := f
+    { obj := fun x => ⟨f x.as⟩
       map := fun {X Y} p => by exact Path.Homotopic.Quotient.mapFn p f
       map_id := fun X => rfl
       map_comp := fun {x y z} p q => by
@@ -356,26 +398,29 @@ theorem map_eq {X Y : TopCat} {x₀ x₁ : X} (f : C(X, Y)) (p : Path.Homotopic.
 /-- Help the typechecker by converting a point in a groupoid back to a point in
 the underlying topological space. -/
 @[reducible]
-def toTop {X : TopCat} (x : πₓ X) : X := x
+def toTop {X : TopCat} (x : πₓ X) : X := x.as
 #align fundamental_groupoid.to_top FundamentalGroupoid.toTop
 
 /-- Help the typechecker by converting a point in a topological space to a
 point in the fundamental groupoid of that space. -/
 @[reducible]
-def fromTop {X : TopCat} (x : X) : πₓ X := x
+def fromTop {X : TopCat} (x : X) : πₓ X := ⟨x⟩
 #align fundamental_groupoid.from_top FundamentalGroupoid.fromTop
 
 /-- Help the typechecker by converting an arrow in the fundamental groupoid of
 a topological space back to a path in that space (i.e., `Path.Homotopic.Quotient`). -/
 -- Porting note: Added `(X := X)` to the type.
 @[reducible]
-def toPath {X : TopCat} {x₀ x₁ : πₓ X} (p : x₀ ⟶ x₁) : Path.Homotopic.Quotient (X := X) x₀ x₁ := p
+def toPath {X : TopCat} {x₀ x₁ : πₓ X} (p : x₀ ⟶ x₁) :
+    Path.Homotopic.Quotient (X := X) x₀.as x₁.as :=
+  p
 #align fundamental_groupoid.to_path FundamentalGroupoid.toPath
 
 /-- Help the typechecker by converting a path in a topological space to an arrow in the
 fundamental groupoid of that space. -/
 @[reducible]
-def fromPath {X : TopCat} {x₀ x₁ : X} (p : Path.Homotopic.Quotient x₀ x₁) : x₀ ⟶ x₁ := p
+def fromPath {X : TopCat} {x₀ x₁ : X} (p : Path.Homotopic.Quotient x₀ x₁) :
+    FundamentalGroupoid.mk x₀ ⟶ FundamentalGroupoid.mk x₁ := p
 #align fundamental_groupoid.from_path FundamentalGroupoid.fromPath
 
 end FundamentalGroupoid

3d7987cd

Revert "chore: revert #7703 (#7710)"

This reverts commit f3695eb2.

ab56fa28

Diff

@@ -324,8 +324,10 @@ def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd where
       map := fun {X Y} p => by exact Path.Homotopic.Quotient.mapFn p f
       map_id := fun X => rfl
       map_comp := fun {x y z} p q => by
-        refine' Quotient.inductionOn₂ p q fun a b => _
-        simp only [comp_eq, ← Path.Homotopic.map_lift, ← Path.Homotopic.comp_lift, Path.map_trans] }
+        refine Quotient.inductionOn₂ p q fun a b => ?_
+        simp only [comp_eq, ← Path.Homotopic.map_lift, ← Path.Homotopic.comp_lift, Path.map_trans]
+        -- This was not needed before leanprover/lean4#2644
+        erw [ ← Path.Homotopic.comp_lift]; rfl}
   map_id X := by
     simp only
     change _ = (⟨_, _, _⟩ : FundamentalGroupoid X ⥤ FundamentalGroupoid X)

3d7987cd

chore: revert #7703 (#7710)

This reverts commit 26eb2b0a.

f3695eb2

Diff

@@ -324,10 +324,8 @@ def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd where
       map := fun {X Y} p => by exact Path.Homotopic.Quotient.mapFn p f
       map_id := fun X => rfl
       map_comp := fun {x y z} p q => by
-        refine Quotient.inductionOn₂ p q fun a b => ?_
-        simp only [comp_eq, ← Path.Homotopic.map_lift, ← Path.Homotopic.comp_lift, Path.map_trans]
-        -- This was not needed before leanprover/lean4#2644
-        erw [ ← Path.Homotopic.comp_lift]; rfl}
+        refine' Quotient.inductionOn₂ p q fun a b => _
+        simp only [comp_eq, ← Path.Homotopic.map_lift, ← Path.Homotopic.comp_lift, Path.map_trans] }
   map_id X := by
     simp only
     change _ = (⟨_, _, _⟩ : FundamentalGroupoid X ⥤ FundamentalGroupoid X)

3d7987cd

chore: bump toolchain to v4.2.0-rc2 (#7703)

This includes all the changes from #7606.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

26eb2b0a

Diff

@@ -324,8 +324,10 @@ def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd where
       map := fun {X Y} p => by exact Path.Homotopic.Quotient.mapFn p f
       map_id := fun X => rfl
       map_comp := fun {x y z} p q => by
-        refine' Quotient.inductionOn₂ p q fun a b => _
-        simp only [comp_eq, ← Path.Homotopic.map_lift, ← Path.Homotopic.comp_lift, Path.map_trans] }
+        refine Quotient.inductionOn₂ p q fun a b => ?_
+        simp only [comp_eq, ← Path.Homotopic.map_lift, ← Path.Homotopic.comp_lift, Path.map_trans]
+        -- This was not needed before leanprover/lean4#2644
+        erw [ ← Path.Homotopic.comp_lift]; rfl}
   map_id X := by
     simp only
     change _ = (⟨_, _, _⟩ : FundamentalGroupoid X ⥤ FundamentalGroupoid X)

3d7987cd

feat: fix norm num with arguments (#6600)

norm_num was passing the wrong syntax node to elabSimpArgs when elaborating, which essentially had the effect of ignoring all arguments it was passed, i.e. norm_num [add_comm] would not try to commute addition in the simp step. The fix itself is very simple (though not obvious to debug!), probably using TSyntax more would help avoid such issues in future.

Due to this bug many norm_num [blah] became rw [blah]; norm_num or similar, sometimes with porting notes, sometimes not, we fix these porting notes and other regressions during the port also.

Interestingly cancel_denoms uses norm_num [<- mul_assoc] internally, so cancel_denoms also got stronger with this change.

49a849ef

Diff

@@ -50,9 +50,7 @@ theorem continuous_reflTransSymmAux : Continuous reflTransSymmAux := by
   · continuity
   · continuity
   intro x hx
-  -- Porting note: norm_num ignores arguments.
-  rw [hx, mul_assoc]
-  norm_num
+  norm_num [hx, mul_assoc]
 #align path.homotopy.continuous_refl_trans_symm_aux Path.Homotopy.continuous_reflTransSymmAux
 
 theorem reflTransSymmAux_mem_I (x : I × I) : reflTransSymmAux x ∈ I := by
@@ -100,9 +98,7 @@ def reflTransSymm (p : Path x₀ x₁) : Homotopy (Path.refl x₀) (p.trans p.sy
       · simp only [Set.Icc.coe_one, one_mul, coe_mk_mk, Function.comp_apply]
         congr 1
         ext
-        -- Porting note: norm_num ignores arguments.
-        simp [sub_sub_eq_add_sub]
-        norm_num
+        norm_num [sub_sub_eq_add_sub]
       · rw [unitInterval.two_mul_sub_one_mem_iff]
         exact ⟨(not_le.1 h).le, unitInterval.le_one x⟩
   prop' t x hx := by
@@ -112,9 +108,7 @@ def reflTransSymm (p : Path x₀ x₁) : Homotopy (Path.refl x₀) (p.trans p.sy
     | inl hx
     | inr hx =>
       rw [hx]
-      simp only [reflTransSymmAux, Set.Icc.coe_zero, Set.Icc.coe_one, one_div, mul_one,
-        inv_nonneg, mul_zero, sub_zero, sub_self, Path.source, Path.target, and_self]
-      norm_num
+      norm_num [reflTransSymmAux]
 #align path.homotopy.refl_trans_symm Path.Homotopy.reflTransSymm
 
 /-- For any path `p` from `x₀` to `x₁`, we have a homotopy from the constant path based at `x₁` to
@@ -137,7 +131,6 @@ theorem continuous_transReflReparamAux : Continuous transReflReparamAux := by
   refine' continuous_if_le _ _ (Continuous.continuousOn _) (Continuous.continuousOn _) _ <;>
     [continuity; continuity; continuity; continuity; skip]
   intro x hx
-  -- Porting note: norm_num ignores arguments.
   simp [hx]
 #align path.homotopy.continuous_trans_refl_reparam_aux Path.Homotopy.continuous_transReflReparamAux
 
@@ -148,15 +141,11 @@ set_option linter.uppercaseLean3 false in
 #align path.homotopy.trans_refl_reparam_aux_mem_I Path.Homotopy.transReflReparamAux_mem_I
 
 theorem transReflReparamAux_zero : transReflReparamAux 0 = 0 := by
-  -- Porting note: norm_num ignores arguments.
-  simp [transReflReparamAux]
-  norm_num
+  norm_num [transReflReparamAux]
 #align path.homotopy.trans_refl_reparam_aux_zero Path.Homotopy.transReflReparamAux_zero
 
 theorem transReflReparamAux_one : transReflReparamAux 1 = 1 := by
-  -- Porting note: norm_num ignores arguments.
-  simp [transReflReparamAux]
-  norm_num
+  norm_num [transReflReparamAux]
 #align path.homotopy.trans_refl_reparam_aux_one Path.Homotopy.transReflReparamAux_one
 
 theorem trans_refl_reparam (p : Path x₀ x₁) :
@@ -203,9 +192,7 @@ theorem continuous_transAssocReparamAux : Continuous transAssocReparamAux := by
     [continuity; continuity; continuity; continuity; continuity; continuity; continuity; skip;
       skip] <;>
     · intro x hx
-      -- Porting note: norm_num ignores arguments.
-      simp [hx]
-      norm_num
+      norm_num [hx]
 #align path.homotopy.continuous_trans_assoc_reparam_aux Path.Homotopy.continuous_transAssocReparamAux
 
 theorem transAssocReparamAux_mem_I (t : I) : transAssocReparamAux t ∈ I := by
@@ -215,15 +202,11 @@ set_option linter.uppercaseLean3 false in
 #align path.homotopy.trans_assoc_reparam_aux_mem_I Path.Homotopy.transAssocReparamAux_mem_I
 
 theorem transAssocReparamAux_zero : transAssocReparamAux 0 = 0 := by
-  -- Porting note: norm_num ignores arguments.
-  simp [transAssocReparamAux]
-  norm_num
+  norm_num [transAssocReparamAux]
 #align path.homotopy.trans_assoc_reparam_aux_zero Path.Homotopy.transAssocReparamAux_zero
 
 theorem transAssocReparamAux_one : transAssocReparamAux 1 = 1 := by
-  -- Porting note: norm_num ignores arguments.
-  simp [transAssocReparamAux]
-  norm_num
+  norm_num [transAssocReparamAux]
 #align path.homotopy.trans_assoc_reparam_aux_one Path.Homotopy.transAssocReparamAux_one
 
 theorem trans_assoc_reparam {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q : Path x₁ x₂) (r : Path x₂ x₃) :

3d7987cd

chore: remove unused simps (#6632)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

916c75c1

Diff

@@ -264,8 +264,7 @@ theorem trans_assoc_reparam {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q :
     linarith
   · exfalso
     linarith
-  · simp only [h₁, if_false, dif_neg (show ¬False from id)]
-    congr
+  · congr
     ring
 #align path.homotopy.trans_assoc_reparam Path.Homotopy.trans_assoc_reparam

3d7987cd

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
-
-! This file was ported from Lean 3 source module algebraic_topology.fundamental_groupoid.basic
-! leanprover-community/mathlib commit 3d7987cda72abc473c7cdbbb075170e9ac620042
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Category.Grpd
 import Mathlib.CategoryTheory.Groupoid
 import Mathlib.Topology.Category.TopCat.Basic
 import Mathlib.Topology.Homotopy.Path
 
+#align_import algebraic_topology.fundamental_groupoid.basic from "leanprover-community/mathlib"@"3d7987cda72abc473c7cdbbb075170e9ac620042"
+
 /-!
 # Fundamental groupoid of a space

3d7987cd

chore: scope notations from category theory. (#5685)

Make sure in particular one can import Mathlib.Tactic for teaching without getting category theory notations in scope. Note that only two files needed an extra open.

5c108f1c

Diff

@@ -22,6 +22,7 @@ homotopy equivalence. With this, the fundamental group of `X` based at `x` is ju
 group of `x`.
 -/
 
+open CategoryTheory
 
 universe u v

3d7987cd

feat: change ConcreteCategory.hasCoeToFun to FunLike (#4693)

b7cba33a

Diff

@@ -345,8 +345,7 @@ def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd where
       map_id := fun X => rfl
       map_comp := fun {x y z} p q => by
         refine' Quotient.inductionOn₂ p q fun a b => _
-        simp only [comp_eq, ← Path.Homotopic.map_lift, ← Path.Homotopic.comp_lift, Path.map_trans]
-        rfl }
+        simp only [comp_eq, ← Path.Homotopic.map_lift, ← Path.Homotopic.comp_lift, Path.map_trans] }
   map_id X := by
     simp only
     change _ = (⟨_, _, _⟩ : FundamentalGroupoid X ⥤ FundamentalGroupoid X)

3d7987cd

chore: fix typos (#4518)

I ran codespell Mathlib and got tired halfway through the suggestions.

92beef58

Diff

@@ -391,7 +391,7 @@ a topological space back to a path in that space (i.e., `Path.Homotopic.Quotient
 def toPath {X : TopCat} {x₀ x₁ : πₓ X} (p : x₀ ⟶ x₁) : Path.Homotopic.Quotient (X := X) x₀ x₁ := p
 #align fundamental_groupoid.to_path FundamentalGroupoid.toPath
 
-/-- Help the typechecker by convering a path in a topological space to an arrow in the
+/-- Help the typechecker by converting a path in a topological space to an arrow in the
 fundamental groupoid of that space. -/
 @[reducible]
 def fromPath {X : TopCat} {x₀ x₁ : X} (p : Path.Homotopic.Quotient x₀ x₁) : x₀ ⟶ x₁ := p

3d7987cd

chore: tidy various files (#4466)

46aa58dc

Diff

@@ -50,8 +50,7 @@ theorem continuous_reflTransSymmAux : Continuous reflTransSymmAux := by
   · continuity
   · continuity
   · continuity
-  · -- Porting note: was `continuity`
-    refine Continuous.mul ?_ (Continuous.sub ?_ ?_) <;> continuity
+  · continuity
   intro x hx
   -- Porting note: norm_num ignores arguments.
   rw [hx, mul_assoc]
@@ -365,13 +364,8 @@ def fundamentalGroupoidFunctor : TopCat ⥤ CategoryTheory.Grpd where
     rfl
 #align fundamental_groupoid.fundamental_groupoid_functor FundamentalGroupoid.fundamentalGroupoidFunctor
 
--- mathport name: fundamental_groupoid_functor
 scoped notation "π" => FundamentalGroupoid.fundamentalGroupoidFunctor
-
--- mathport name: fundamental_groupoid_functor.obj
 scoped notation "πₓ" => FundamentalGroupoid.fundamentalGroupoidFunctor.obj
-
--- mathport name: fundamental_groupoid_functor.map
 scoped notation "πₘ" => FundamentalGroupoid.fundamentalGroupoidFunctor.map
 
 theorem map_eq {X Y : TopCat} {x₀ x₁ : X} (f : C(X, Y)) (p : Path.Homotopic.Quotient x₀ x₁) :

3d7987cd

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -176,7 +176,7 @@ theorem trans_refl_reparam (p : Path x₀ x₁) :
   · simp
 #align path.homotopy.trans_refl_reparam Path.Homotopy.trans_refl_reparam
 
-/-- For any path `p` from `x₀` to `x₁`, we have a homotopy from `p.trans (path.refl x₁)` to `p`. -/
+/-- For any path `p` from `x₀` to `x₁`, we have a homotopy from `p.trans (Path.refl x₁)` to `p`. -/
 def transRefl (p : Path x₀ x₁) : Homotopy (p.trans (Path.refl x₁)) p :=
   ((Homotopy.reparam p (fun t => ⟨transReflReparamAux t, transReflReparamAux_mem_I t⟩)
           (by continuity) (Subtype.ext transReflReparamAux_zero)

3d7987cd

chore: update std 05-22 (#4248)

The main breaking change is that tac <;> [t1, t2] is now written tac <;> [t1; t2], to avoid clashing with tactics like cases and use that take comma-separated lists.

ac36b28e

Diff

@@ -138,7 +138,7 @@ def transReflReparamAux (t : I) : ℝ :=
 @[continuity]
 theorem continuous_transReflReparamAux : Continuous transReflReparamAux := by
   refine' continuous_if_le _ _ (Continuous.continuousOn _) (Continuous.continuousOn _) _ <;>
-    [continuity, continuity, continuity, continuity, skip]
+    [continuity; continuity; continuity; continuity; skip]
   intro x hx
   -- Porting note: norm_num ignores arguments.
   simp [hx]
@@ -203,7 +203,7 @@ theorem continuous_transAssocReparamAux : Continuous transAssocReparamAux := by
   refine' continuous_if_le _ _ (Continuous.continuousOn _)
       (continuous_if_le _ _ (Continuous.continuousOn _) (Continuous.continuousOn _) _).continuousOn
       _ <;>
-    [continuity, continuity, continuity, continuity, continuity, continuity, continuity, skip,
+    [continuity; continuity; continuity; continuity; continuity; continuity; continuity; skip;
       skip] <;>
     · intro x hx
       -- Porting note: norm_num ignores arguments.

3d7987cd

chore: rename Top->TopCat (#4089)

6fbdb197

Diff

@@ -10,7 +10,7 @@ Authors: Shing Tak Lam
 -/
 import Mathlib.CategoryTheory.Category.Grpd
 import Mathlib.CategoryTheory.Groupoid
-import Mathlib.Topology.Category.Top.Basic
+import Mathlib.Topology.Category.TopCat.Basic
 import Mathlib.Topology.Homotopy.Path
 
 /-!

3d7987cd

feat: port AlgebraicTopology.FundamentalGroupoid.Basic (#3955)

Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>

905ac032

`algebraic_topology.fundamental_groupoid.basic` ⟷ `Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 637

algebraic_topology.fundamental_groupoid.basic ⟷ Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 637

`algebraic_topology.fundamental_groupoid.basic` ⟷ `Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic`