category_theory.category.Groupoid
⟷
Mathlib.CategoryTheory.Category.Grpd
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -102,9 +102,9 @@ def forgetToCat : Grpd.{v, u} ⥤ Cat.{v, u}
#align category_theory.Groupoid.forget_to_Cat CategoryTheory.Grpd.forgetToCat
-/
-#print CategoryTheory.Grpd.forgetToCatFull /-
-instance forgetToCatFull : CategoryTheory.Functor.Full forgetToCat where preimage C D := id
-#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.Grpd.forgetToCatFull
+#print CategoryTheory.Grpd.forgetToCat_full /-
+instance forgetToCat_full : CategoryTheory.Functor.Full forgetToCat where preimage C D := id
+#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.Grpd.forgetToCat_full
-/
#print CategoryTheory.Grpd.forgetToCat_faithful /-
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -103,12 +103,12 @@ def forgetToCat : Grpd.{v, u} ⥤ Cat.{v, u}
-/
#print CategoryTheory.Grpd.forgetToCatFull /-
-instance forgetToCatFull : Full forgetToCat where preimage C D := id
+instance forgetToCatFull : CategoryTheory.Functor.Full forgetToCat where preimage C D := id
#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.Grpd.forgetToCatFull
-/
#print CategoryTheory.Grpd.forgetToCat_faithful /-
-instance forgetToCat_faithful : Faithful forgetToCat where
+instance forgetToCat_faithful : CategoryTheory.Functor.Faithful forgetToCat where
#align category_theory.Groupoid.forget_to_Cat_faithful CategoryTheory.Grpd.forgetToCat_faithful
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,10 +3,10 @@ Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathbin.CategoryTheory.SingleObj
-import Mathbin.CategoryTheory.Limits.Shapes.Products
-import Mathbin.CategoryTheory.Pi.Basic
-import Mathbin.CategoryTheory.Limits.IsLimit
+import CategoryTheory.SingleObj
+import CategoryTheory.Limits.Shapes.Products
+import CategoryTheory.Pi.Basic
+import CategoryTheory.Limits.IsLimit
#align_import category_theory.category.Groupoid from "leanprover-community/mathlib"@"fe8d0ff42c3c24d789f491dc2622b6cac3d61564"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,17 +2,14 @@
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module category_theory.category.Groupoid
-! leanprover-community/mathlib commit fe8d0ff42c3c24d789f491dc2622b6cac3d61564
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.SingleObj
import Mathbin.CategoryTheory.Limits.Shapes.Products
import Mathbin.CategoryTheory.Pi.Basic
import Mathbin.CategoryTheory.Limits.IsLimit
+#align_import category_theory.category.Groupoid from "leanprover-community/mathlib"@"fe8d0ff42c3c24d789f491dc2622b6cac3d61564"
+
/-!
# Category of groupoids
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -67,10 +67,12 @@ def of (C : Type u) [Groupoid.{v} C] : Grpd.{v, u} :=
#align category_theory.Groupoid.of CategoryTheory.Grpd.of
-/
+#print CategoryTheory.Grpd.coe_of /-
@[simp]
theorem coe_of (C : Type u) [Groupoid C] : (of C : Type u) = C :=
rfl
#align category_theory.Groupoid.coe_of CategoryTheory.Grpd.coe_of
+-/
#print CategoryTheory.Grpd.category /-
/-- Category structure on `Groupoid` -/
@@ -103,11 +105,15 @@ def forgetToCat : Grpd.{v, u} ⥤ Cat.{v, u}
#align category_theory.Groupoid.forget_to_Cat CategoryTheory.Grpd.forgetToCat
-/
+#print CategoryTheory.Grpd.forgetToCatFull /-
instance forgetToCatFull : Full forgetToCat where preimage C D := id
#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.Grpd.forgetToCatFull
+-/
+#print CategoryTheory.Grpd.forgetToCat_faithful /-
instance forgetToCat_faithful : Faithful forgetToCat where
#align category_theory.Groupoid.forget_to_Cat_faithful CategoryTheory.Grpd.forgetToCat_faithful
+-/
#print CategoryTheory.Grpd.hom_to_functor /-
/-- Convert arrows in the category of groupoids to functors,
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -139,7 +139,7 @@ def piLimitFan ⦃J : Type u⦄ (F : J → Grpd.{u, u}) : Limits.Fan F :=
/-- The product fan over an indexed family of groupoids, is a limit cone. -/
def piLimitFanIsLimit ⦃J : Type u⦄ (F : J → Grpd.{u, u}) : Limits.IsLimit (piLimitFan F) :=
Limits.mkFanLimit (piLimitFan F) (fun s => Functor.pi' fun j => s.proj j)
- (by intros ; dsimp only [pi_limit_fan]; simp [hom_to_functor])
+ (by intros; dsimp only [pi_limit_fan]; simp [hom_to_functor])
(by
intro s m w
apply functor.pi_ext
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -67,12 +67,6 @@ def of (C : Type u) [Groupoid.{v} C] : Grpd.{v, u} :=
#align category_theory.Groupoid.of CategoryTheory.Grpd.of
-/
-/- warning: category_theory.Groupoid.coe_of -> CategoryTheory.Grpd.coe_of is a dubious translation:
-lean 3 declaration is
- forall (C : Type.{u1}) [_inst_1 : CategoryTheory.Groupoid.{u2, u1} C], Eq.{succ (succ u1)} Type.{u1} (coeSort.{succ (max (succ u1) u1 (succ u2)), succ (succ u1)} CategoryTheory.Grpd.{u2, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u2} (CategoryTheory.Grpd.of.{u2, u1} C _inst_1)) C
-but is expected to have type
- forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Groupoid.{u1, u2} C], Eq.{succ (succ u2)} Type.{u2} (CategoryTheory.Bundled.α.{u2, max u2 (succ u1)} CategoryTheory.Groupoid.{u1, u2} (CategoryTheory.Grpd.of.{u1, u2} C _inst_1)) C
-Case conversion may be inaccurate. Consider using '#align category_theory.Groupoid.coe_of CategoryTheory.Grpd.coe_ofₓ'. -/
@[simp]
theorem coe_of (C : Type u) [Groupoid C] : (of C : Type u) = C :=
rfl
@@ -109,21 +103,9 @@ def forgetToCat : Grpd.{v, u} ⥤ Cat.{v, u}
#align category_theory.Groupoid.forget_to_Cat CategoryTheory.Grpd.forgetToCat
-/
-/- warning: category_theory.Groupoid.forget_to_Cat_full -> CategoryTheory.Grpd.forgetToCatFull is a dubious translation:
-lean 3 declaration is
- CategoryTheory.Full.{max u1 u2, max u1 u2, max (succ u2) u2 (succ u1), max (succ u2) u2 (succ u1)} CategoryTheory.Grpd.{u1, u2} CategoryTheory.Grpd.category.{u1, u2} CategoryTheory.Cat.{u1, u2} CategoryTheory.Cat.category.{u1, u2} CategoryTheory.Grpd.forgetToCat.{u1, u2}
-but is expected to have type
- CategoryTheory.Full.{max u1 u2, max u1 u2, max (succ u1) (succ u2), max (succ u1) (succ u2)} CategoryTheory.Grpd.{u2, u1} CategoryTheory.Grpd.category.{u2, u1} CategoryTheory.Cat.{u2, u1} CategoryTheory.Cat.category.{u2, u1} CategoryTheory.Grpd.forgetToCat.{u2, u1}
-Case conversion may be inaccurate. Consider using '#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.Grpd.forgetToCatFullₓ'. -/
instance forgetToCatFull : Full forgetToCat where preimage C D := id
#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.Grpd.forgetToCatFull
-/- warning: category_theory.Groupoid.forget_to_Cat_faithful -> CategoryTheory.Grpd.forgetToCat_faithful is a dubious translation:
-lean 3 declaration is
- CategoryTheory.Faithful.{max u1 u2, max u1 u2, max (succ u2) u2 (succ u1), max (succ u2) u2 (succ u1)} CategoryTheory.Grpd.{u1, u2} CategoryTheory.Grpd.category.{u1, u2} CategoryTheory.Cat.{u1, u2} CategoryTheory.Cat.category.{u1, u2} CategoryTheory.Grpd.forgetToCat.{u1, u2}
-but is expected to have type
- CategoryTheory.Faithful.{max u1 u2, max u1 u2, max (succ u1) (succ u2), max (succ u1) (succ u2)} CategoryTheory.Grpd.{u2, u1} CategoryTheory.Grpd.category.{u2, u1} CategoryTheory.Cat.{u2, u1} CategoryTheory.Cat.category.{u2, u1} CategoryTheory.Grpd.forgetToCat.{u2, u1}
-Case conversion may be inaccurate. Consider using '#align category_theory.Groupoid.forget_to_Cat_faithful CategoryTheory.Grpd.forgetToCat_faithfulₓ'. -/
instance forgetToCat_faithful : Faithful forgetToCat where
#align category_theory.Groupoid.forget_to_Cat_faithful CategoryTheory.Grpd.forgetToCat_faithful
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -157,10 +157,7 @@ def piLimitFan ⦃J : Type u⦄ (F : J → Grpd.{u, u}) : Limits.Fan F :=
/-- The product fan over an indexed family of groupoids, is a limit cone. -/
def piLimitFanIsLimit ⦃J : Type u⦄ (F : J → Grpd.{u, u}) : Limits.IsLimit (piLimitFan F) :=
Limits.mkFanLimit (piLimitFan F) (fun s => Functor.pi' fun j => s.proj j)
- (by
- intros
- dsimp only [pi_limit_fan]
- simp [hom_to_functor])
+ (by intros ; dsimp only [pi_limit_fan]; simp [hom_to_functor])
(by
intro s m w
apply functor.pi_ext
@@ -187,10 +184,7 @@ noncomputable def piIsoPi (J : Type u) (f : J → Grpd.{u, u}) : @of (∀ j, f j
#print CategoryTheory.Grpd.piIsoPi_hom_π /-
@[simp]
theorem piIsoPi_hom_π (J : Type u) (f : J → Grpd.{u, u}) (j : J) :
- (piIsoPi J f).Hom ≫ Limits.Pi.π f j = CategoryTheory.Pi.eval _ j :=
- by
- simp [pi_iso_pi]
- rfl
+ (piIsoPi J f).Hom ≫ Limits.Pi.π f j = CategoryTheory.Pi.eval _ j := by simp [pi_iso_pi]; rfl
#align category_theory.Groupoid.pi_iso_pi_hom_π CategoryTheory.Grpd.piIsoPi_hom_π
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
! This file was ported from Lean 3 source module category_theory.category.Groupoid
-! leanprover-community/mathlib commit c9c9fa15fec7ca18e9ec97306fb8764bfe988a7e
+! leanprover-community/mathlib commit fe8d0ff42c3c24d789f491dc2622b6cac3d61564
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -16,6 +16,9 @@ import Mathbin.CategoryTheory.Limits.IsLimit
/-!
# Category of groupoids
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file contains the definition of the category `Groupoid` of all groupoids.
In this category objects are groupoids and morphisms are functors
between these groupoids.
mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab
@@ -34,37 +34,50 @@ universe v u
namespace CategoryTheory
+#print CategoryTheory.Grpd /-
-- intended to be used with explicit universe parameters
/-- Category of groupoids -/
@[nolint check_univs]
-def GroupoidCat :=
+def Grpd :=
Bundled Groupoid.{v, u}
-#align category_theory.Groupoid CategoryTheory.GroupoidCat
+#align category_theory.Groupoid CategoryTheory.Grpd
+-/
namespace Groupoid
-instance : Inhabited GroupoidCat :=
+instance : Inhabited Grpd :=
⟨Bundled.of (SingleObj PUnit)⟩
-instance str (C : GroupoidCat.{v, u}) : Groupoid.{v, u} C.α :=
+#print CategoryTheory.Grpd.str' /-
+instance str' (C : Grpd.{v, u}) : Groupoid.{v, u} C.α :=
C.str
-#align category_theory.Groupoid.str CategoryTheory.GroupoidCat.str
+#align category_theory.Groupoid.str CategoryTheory.Grpd.str'
+-/
-instance : CoeSort GroupoidCat (Type _) :=
+instance : CoeSort Grpd (Type _) :=
Bundled.hasCoeToSort
+#print CategoryTheory.Grpd.of /-
/-- Construct a bundled `Groupoid` from the underlying type and the typeclass. -/
-def of (C : Type u) [Groupoid.{v} C] : GroupoidCat.{v, u} :=
+def of (C : Type u) [Groupoid.{v} C] : Grpd.{v, u} :=
Bundled.of C
-#align category_theory.Groupoid.of CategoryTheory.GroupoidCat.of
+#align category_theory.Groupoid.of CategoryTheory.Grpd.of
+-/
+/- warning: category_theory.Groupoid.coe_of -> CategoryTheory.Grpd.coe_of is a dubious translation:
+lean 3 declaration is
+ forall (C : Type.{u1}) [_inst_1 : CategoryTheory.Groupoid.{u2, u1} C], Eq.{succ (succ u1)} Type.{u1} (coeSort.{succ (max (succ u1) u1 (succ u2)), succ (succ u1)} CategoryTheory.Grpd.{u2, u1} Type.{u1} CategoryTheory.Grpd.hasCoeToSort.{u1, u2} (CategoryTheory.Grpd.of.{u2, u1} C _inst_1)) C
+but is expected to have type
+ forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Groupoid.{u1, u2} C], Eq.{succ (succ u2)} Type.{u2} (CategoryTheory.Bundled.α.{u2, max u2 (succ u1)} CategoryTheory.Groupoid.{u1, u2} (CategoryTheory.Grpd.of.{u1, u2} C _inst_1)) C
+Case conversion may be inaccurate. Consider using '#align category_theory.Groupoid.coe_of CategoryTheory.Grpd.coe_ofₓ'. -/
@[simp]
theorem coe_of (C : Type u) [Groupoid C] : (of C : Type u) = C :=
rfl
-#align category_theory.Groupoid.coe_of CategoryTheory.GroupoidCat.coe_of
+#align category_theory.Groupoid.coe_of CategoryTheory.Grpd.coe_of
+#print CategoryTheory.Grpd.category /-
/-- Category structure on `Groupoid` -/
-instance category : LargeCategory.{max v u} GroupoidCat.{v, u}
+instance category : LargeCategory.{max v u} Grpd.{v, u}
where
Hom C D := C ⥤ D
id C := 𝟭 C
@@ -72,51 +85,74 @@ instance category : LargeCategory.{max v u} GroupoidCat.{v, u}
id_comp' C D F := by cases F <;> rfl
comp_id' C D F := by cases F <;> rfl
assoc' := by intros <;> rfl
-#align category_theory.Groupoid.category CategoryTheory.GroupoidCat.category
+#align category_theory.Groupoid.category CategoryTheory.Grpd.category
+-/
+#print CategoryTheory.Grpd.objects /-
/-- Functor that gets the set of objects of a groupoid. It is not
called `forget`, because it is not a faithful functor. -/
-def objects : GroupoidCat.{v, u} ⥤ Type u
- where
+def objects : Grpd.{v, u} ⥤ Type u where
obj := Bundled.α
map C D F := F.obj
-#align category_theory.Groupoid.objects CategoryTheory.GroupoidCat.objects
+#align category_theory.Groupoid.objects CategoryTheory.Grpd.objects
+-/
+#print CategoryTheory.Grpd.forgetToCat /-
/-- Forgetting functor to `Cat` -/
-def forgetToCat : GroupoidCat.{v, u} ⥤ Cat.{v, u}
+def forgetToCat : Grpd.{v, u} ⥤ Cat.{v, u}
where
obj C := Cat.of C
map C D := id
-#align category_theory.Groupoid.forget_to_Cat CategoryTheory.GroupoidCat.forgetToCat
+#align category_theory.Groupoid.forget_to_Cat CategoryTheory.Grpd.forgetToCat
+-/
+/- warning: category_theory.Groupoid.forget_to_Cat_full -> CategoryTheory.Grpd.forgetToCatFull is a dubious translation:
+lean 3 declaration is
+ CategoryTheory.Full.{max u1 u2, max u1 u2, max (succ u2) u2 (succ u1), max (succ u2) u2 (succ u1)} CategoryTheory.Grpd.{u1, u2} CategoryTheory.Grpd.category.{u1, u2} CategoryTheory.Cat.{u1, u2} CategoryTheory.Cat.category.{u1, u2} CategoryTheory.Grpd.forgetToCat.{u1, u2}
+but is expected to have type
+ CategoryTheory.Full.{max u1 u2, max u1 u2, max (succ u1) (succ u2), max (succ u1) (succ u2)} CategoryTheory.Grpd.{u2, u1} CategoryTheory.Grpd.category.{u2, u1} CategoryTheory.Cat.{u2, u1} CategoryTheory.Cat.category.{u2, u1} CategoryTheory.Grpd.forgetToCat.{u2, u1}
+Case conversion may be inaccurate. Consider using '#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.Grpd.forgetToCatFullₓ'. -/
instance forgetToCatFull : Full forgetToCat where preimage C D := id
-#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.GroupoidCat.forgetToCatFull
-
+#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.Grpd.forgetToCatFull
+
+/- warning: category_theory.Groupoid.forget_to_Cat_faithful -> CategoryTheory.Grpd.forgetToCat_faithful is a dubious translation:
+lean 3 declaration is
+ CategoryTheory.Faithful.{max u1 u2, max u1 u2, max (succ u2) u2 (succ u1), max (succ u2) u2 (succ u1)} CategoryTheory.Grpd.{u1, u2} CategoryTheory.Grpd.category.{u1, u2} CategoryTheory.Cat.{u1, u2} CategoryTheory.Cat.category.{u1, u2} CategoryTheory.Grpd.forgetToCat.{u1, u2}
+but is expected to have type
+ CategoryTheory.Faithful.{max u1 u2, max u1 u2, max (succ u1) (succ u2), max (succ u1) (succ u2)} CategoryTheory.Grpd.{u2, u1} CategoryTheory.Grpd.category.{u2, u1} CategoryTheory.Cat.{u2, u1} CategoryTheory.Cat.category.{u2, u1} CategoryTheory.Grpd.forgetToCat.{u2, u1}
+Case conversion may be inaccurate. Consider using '#align category_theory.Groupoid.forget_to_Cat_faithful CategoryTheory.Grpd.forgetToCat_faithfulₓ'. -/
instance forgetToCat_faithful : Faithful forgetToCat where
-#align category_theory.Groupoid.forget_to_Cat_faithful CategoryTheory.GroupoidCat.forgetToCat_faithful
+#align category_theory.Groupoid.forget_to_Cat_faithful CategoryTheory.Grpd.forgetToCat_faithful
+#print CategoryTheory.Grpd.hom_to_functor /-
/-- Convert arrows in the category of groupoids to functors,
which sometimes helps in applying simp lemmas -/
-theorem hom_to_functor {C D E : GroupoidCat.{v, u}} (f : C ⟶ D) (g : D ⟶ E) : f ≫ g = f ⋙ g :=
+theorem hom_to_functor {C D E : Grpd.{v, u}} (f : C ⟶ D) (g : D ⟶ E) : f ≫ g = f ⋙ g :=
rfl
-#align category_theory.Groupoid.hom_to_functor CategoryTheory.GroupoidCat.hom_to_functor
+#align category_theory.Groupoid.hom_to_functor CategoryTheory.Grpd.hom_to_functor
+-/
+#print CategoryTheory.Grpd.id_to_functor /-
/-- Converts identity in the category of groupoids to the functor identity -/
-theorem id_to_functor {C : GroupoidCat.{v, u}} : 𝟭 C = 𝟙 C :=
+theorem id_to_functor {C : Grpd.{v, u}} : 𝟭 C = 𝟙 C :=
rfl
-#align category_theory.Groupoid.id_to_functor CategoryTheory.GroupoidCat.id_to_functor
+#align category_theory.Groupoid.id_to_functor CategoryTheory.Grpd.id_to_functor
+-/
section Products
attribute [local tidy] tactic.discrete_cases
+#print CategoryTheory.Grpd.piLimitFan /-
/-- Construct the product over an indexed family of groupoids, as a fan. -/
-def piLimitFan ⦃J : Type u⦄ (F : J → GroupoidCat.{u, u}) : Limits.Fan F :=
+def piLimitFan ⦃J : Type u⦄ (F : J → Grpd.{u, u}) : Limits.Fan F :=
Limits.Fan.mk (@of (∀ j : J, F j) _) fun j => CategoryTheory.Pi.eval _ j
-#align category_theory.Groupoid.pi_limit_fan CategoryTheory.GroupoidCat.piLimitFan
+#align category_theory.Groupoid.pi_limit_fan CategoryTheory.Grpd.piLimitFan
+-/
+#print CategoryTheory.Grpd.piLimitFanIsLimit /-
/-- The product fan over an indexed family of groupoids, is a limit cone. -/
-def piLimitFanIsLimit ⦃J : Type u⦄ (F : J → GroupoidCat.{u, u}) : Limits.IsLimit (piLimitFan F) :=
+def piLimitFanIsLimit ⦃J : Type u⦄ (F : J → Grpd.{u, u}) : Limits.IsLimit (piLimitFan F) :=
Limits.mkFanLimit (piLimitFan F) (fun s => Functor.pi' fun j => s.proj j)
(by
intros
@@ -127,26 +163,33 @@ def piLimitFanIsLimit ⦃J : Type u⦄ (F : J → GroupoidCat.{u, u}) : Limits.I
apply functor.pi_ext
intro j; specialize w j
simpa)
-#align category_theory.Groupoid.pi_limit_fan_is_limit CategoryTheory.GroupoidCat.piLimitFanIsLimit
+#align category_theory.Groupoid.pi_limit_fan_is_limit CategoryTheory.Grpd.piLimitFanIsLimit
+-/
-instance has_pi : Limits.HasProducts GroupoidCat.{u, u} :=
+#print CategoryTheory.Grpd.has_pi /-
+instance has_pi : Limits.HasProducts Grpd.{u, u} :=
Limits.hasProducts_of_limit_fans piLimitFan piLimitFanIsLimit
-#align category_theory.Groupoid.has_pi CategoryTheory.GroupoidCat.has_pi
+#align category_theory.Groupoid.has_pi CategoryTheory.Grpd.has_pi
+-/
+#print CategoryTheory.Grpd.piIsoPi /-
/-- The product of a family of groupoids is isomorphic
to the product object in the category of Groupoids -/
-noncomputable def piIsoPi (J : Type u) (f : J → GroupoidCat.{u, u}) : @of (∀ j, f j) _ ≅ ∏ f :=
+noncomputable def piIsoPi (J : Type u) (f : J → Grpd.{u, u}) : @of (∀ j, f j) _ ≅ ∏ f :=
Limits.IsLimit.conePointUniqueUpToIso (piLimitFanIsLimit f)
(Limits.limit.isLimit (Discrete.functor f))
-#align category_theory.Groupoid.pi_iso_pi CategoryTheory.GroupoidCat.piIsoPi
+#align category_theory.Groupoid.pi_iso_pi CategoryTheory.Grpd.piIsoPi
+-/
+#print CategoryTheory.Grpd.piIsoPi_hom_π /-
@[simp]
-theorem piIsoPi_hom_π (J : Type u) (f : J → GroupoidCat.{u, u}) (j : J) :
+theorem piIsoPi_hom_π (J : Type u) (f : J → Grpd.{u, u}) (j : J) :
(piIsoPi J f).Hom ≫ Limits.Pi.π f j = CategoryTheory.Pi.eval _ j :=
by
simp [pi_iso_pi]
rfl
-#align category_theory.Groupoid.pi_iso_pi_hom_π CategoryTheory.GroupoidCat.piIsoPi_hom_π
+#align category_theory.Groupoid.pi_iso_pi_hom_π CategoryTheory.Grpd.piIsoPi_hom_π
+-/
end Products
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Functor.Full
a Prop (#12449)
Before this PR, Functor.Full
contained the data of the preimage of maps by a full functor F
. This PR makes Functor.Full
a proposition. This is to prevent any diamond to appear.
The lemma Functor.image_preimage
is also renamed Functor.map_preimage
.
Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
@@ -91,9 +91,9 @@ def forgetToCat : Grpd.{v, u} ⥤ Cat.{v, u} where
set_option linter.uppercaseLean3 false in
#align category_theory.Groupoid.forget_to_Cat CategoryTheory.Grpd.forgetToCat
-instance forgetToCatFull : forgetToCat.Full where preimage := id
+instance forgetToCat_full : forgetToCat.Full where map_surjective f := ⟨f, rfl⟩
set_option linter.uppercaseLean3 false in
-#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.Grpd.forgetToCatFull
+#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.Grpd.forgetToCat_full
instance forgetToCat_faithful : forgetToCat.Faithful where
set_option linter.uppercaseLean3 false in
These notions on functors are now Functor.Full
, Functor.Faithful
, Functor.EssSurj
, Functor.IsEquivalence
, Functor.ReflectsIsomorphisms
. Deprecated aliases are introduced for the previous names.
@@ -91,11 +91,11 @@ def forgetToCat : Grpd.{v, u} ⥤ Cat.{v, u} where
set_option linter.uppercaseLean3 false in
#align category_theory.Groupoid.forget_to_Cat CategoryTheory.Grpd.forgetToCat
-instance forgetToCatFull : Full forgetToCat where preimage := id
+instance forgetToCatFull : forgetToCat.Full where preimage := id
set_option linter.uppercaseLean3 false in
#align category_theory.Groupoid.forget_to_Cat_full CategoryTheory.Grpd.forgetToCatFull
-instance forgetToCat_faithful : Faithful forgetToCat where
+instance forgetToCat_faithful : forgetToCat.Faithful where
set_option linter.uppercaseLean3 false in
#align category_theory.Groupoid.forget_to_Cat_faithful CategoryTheory.Grpd.forgetToCat_faithful
@@ -70,8 +70,8 @@ instance category : LargeCategory.{max v u} Grpd.{v, u} where
Hom C D := C ⥤ D
id C := 𝟭 C
comp F G := F ⋙ G
- id_comp _ := by rfl
- comp_id _ := by rfl
+ id_comp _ := rfl
+ comp_id _ := rfl
assoc := by intros; rfl
set_option linter.uppercaseLean3 false in
#align category_theory.Groupoid.category CategoryTheory.Grpd.category
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -50,7 +50,7 @@ instance str' (C : Grpd.{v, u}) : Groupoid.{v, u} C.α :=
set_option linter.uppercaseLean3 false in
#align category_theory.Groupoid.str CategoryTheory.Grpd.str'
-instance : CoeSort Grpd (Type _) :=
+instance : CoeSort Grpd (Type*) :=
Bundled.coeSort
/-- Construct a bundled `Grpd` from the underlying type and the typeclass `Groupoid`. -/
@@ -2,17 +2,14 @@
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module category_theory.category.Groupoid
-! leanprover-community/mathlib commit c9c9fa15fec7ca18e9ec97306fb8764bfe988a7e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.SingleObj
import Mathlib.CategoryTheory.Limits.Shapes.Products
import Mathlib.CategoryTheory.Pi.Basic
import Mathlib.CategoryTheory.Limits.IsLimit
+#align_import category_theory.category.Groupoid from "leanprover-community/mathlib"@"c9c9fa15fec7ca18e9ec97306fb8764bfe988a7e"
+
/-!
# Category of groupoids
This is the second half of the changes originally in #5699, removing all occurrences of ;
after a space and implementing a linter rule to enforce it.
In most cases this 2-character substring has a space after it, so the following command was run first:
find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;
The remaining cases were few enough in number that they were done manually.
@@ -75,7 +75,7 @@ instance category : LargeCategory.{max v u} Grpd.{v, u} where
comp F G := F ⋙ G
id_comp _ := by rfl
comp_id _ := by rfl
- assoc := by intros ; rfl
+ assoc := by intros; rfl
set_option linter.uppercaseLean3 false in
#align category_theory.Groupoid.category CategoryTheory.Grpd.category
@@ -117,8 +117,6 @@ set_option linter.uppercaseLean3 false in
section Products
---attribute [local tidy] tactic.discrete_cases
-
/-- Construct the product over an indexed family of groupoids, as a fan. -/
def piLimitFan ⦃J : Type u⦄ (F : J → Grpd.{u, u}) : Limits.Fan F :=
Limits.Fan.mk (@of (∀ j : J, F j) _) fun j => CategoryTheory.Pi.eval _ j
The unported dependencies are