category_theory.limits.preserves.shapes.pullbacks
⟷
Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks
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/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Andrew Yang
-/
-import Mathbin.CategoryTheory.Limits.Shapes.Pullbacks
-import Mathbin.CategoryTheory.Limits.Preserves.Basic
+import CategoryTheory.Limits.Shapes.Pullbacks
+import CategoryTheory.Limits.Preserves.Basic
#align_import category_theory.limits.preserves.shapes.pullbacks from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Andrew Yang
-
-! This file was ported from Lean 3 source module category_theory.limits.preserves.shapes.pullbacks
-! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Limits.Shapes.Pullbacks
import Mathbin.CategoryTheory.Limits.Preserves.Basic
+#align_import category_theory.limits.preserves.shapes.pullbacks from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
/-!
# Preserving pullbacks
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -50,6 +50,7 @@ variable (G : C ⥤ D)
variable {W X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z} {h : W ⟶ X} {k : W ⟶ Y} (comm : h ≫ f = k ≫ g)
+#print CategoryTheory.Limits.isLimitMapConePullbackConeEquiv /-
/-- The map of a pullback cone is a limit iff the fork consisting of the mapped morphisms is a
limit. This essentially lets us commute `pullback_cone.mk` with `functor.map_cone`. -/
def isLimitMapConePullbackConeEquiv :
@@ -62,27 +63,34 @@ def isLimitMapConePullbackConeEquiv :
Cones.ext (Iso.refl _) <| by
rintro (_ | _ | _) <;> dsimp <;> simp only [comp_id, id_comp, G.map_comp]
#align category_theory.limits.is_limit_map_cone_pullback_cone_equiv CategoryTheory.Limits.isLimitMapConePullbackConeEquiv
+-/
+#print CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimit /-
/-- The property of preserving pullbacks expressed in terms of binary fans. -/
def isLimitPullbackConeMapOfIsLimit [PreservesLimit (cospan f g) G]
(l : IsLimit (PullbackCone.mk h k comm)) : IsLimit (PullbackCone.mk (G.map h) (G.map k) _) :=
isLimitMapConePullbackConeEquiv G comm (PreservesLimit.preserves l)
#align category_theory.limits.is_limit_pullback_cone_map_of_is_limit CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimit
+-/
+#print CategoryTheory.Limits.isLimitOfIsLimitPullbackConeMap /-
/-- The property of reflecting pullbacks expressed in terms of binary fans. -/
def isLimitOfIsLimitPullbackConeMap [ReflectsLimit (cospan f g) G]
(l : IsLimit (PullbackCone.mk (G.map h) (G.map k) _)) : IsLimit (PullbackCone.mk h k comm) :=
ReflectsLimit.reflects ((isLimitMapConePullbackConeEquiv G comm).symm l)
#align category_theory.limits.is_limit_of_is_limit_pullback_cone_map CategoryTheory.Limits.isLimitOfIsLimitPullbackConeMap
+-/
variable (f g) [PreservesLimit (cospan f g) G]
+#print CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimit /-
/-- If `G` preserves pullbacks and `C` has them, then the pullback cone constructed of the mapped
morphisms of the pullback cone is a limit. -/
def isLimitOfHasPullbackOfPreservesLimit [HasPullback f g] :
IsLimit (PullbackCone.mk (G.map pullback.fst) (G.map pullback.snd) _) :=
isLimitPullbackConeMapOfIsLimit G _ (pullbackIsPullback f g)
#align category_theory.limits.is_limit_of_has_pullback_of_preserves_limit CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimit
+-/
#print CategoryTheory.Limits.preservesPullbackSymmetry /-
/-- If `F` preserves the pullback of `f, g`, it also preserves the pullback of `g, f`. -/
@@ -105,41 +113,53 @@ def preservesPullbackSymmetry : PreservesLimit (cospan g f) G
#align category_theory.limits.preserves_pullback_symmetry CategoryTheory.Limits.preservesPullbackSymmetry
-/
+#print CategoryTheory.Limits.hasPullback_of_preservesPullback /-
theorem hasPullback_of_preservesPullback [HasPullback f g] : HasPullback (G.map f) (G.map g) :=
⟨⟨⟨_, isLimitPullbackConeMapOfIsLimit G _ (pullbackIsPullback _ _)⟩⟩⟩
#align category_theory.limits.has_pullback_of_preserves_pullback CategoryTheory.Limits.hasPullback_of_preservesPullback
+-/
variable [HasPullback f g] [HasPullback (G.map f) (G.map g)]
+#print CategoryTheory.Limits.PreservesPullback.iso /-
/-- If `G` preserves the pullback of `(f,g)`, then the pullback comparison map for `G` at `(f,g)` is
an isomorphism. -/
def PreservesPullback.iso : G.obj (pullback f g) ≅ pullback (G.map f) (G.map g) :=
IsLimit.conePointUniqueUpToIso (isLimitOfHasPullbackOfPreservesLimit G f g) (limit.isLimit _)
#align category_theory.limits.preserves_pullback.iso CategoryTheory.Limits.PreservesPullback.iso
+-/
+#print CategoryTheory.Limits.PreservesPullback.iso_hom_fst /-
@[reassoc]
theorem PreservesPullback.iso_hom_fst :
(PreservesPullback.iso G f g).Hom ≫ pullback.fst = G.map pullback.fst := by
simp [preserves_pullback.iso]
#align category_theory.limits.preserves_pullback.iso_hom_fst CategoryTheory.Limits.PreservesPullback.iso_hom_fst
+-/
+#print CategoryTheory.Limits.PreservesPullback.iso_hom_snd /-
@[reassoc]
theorem PreservesPullback.iso_hom_snd :
(PreservesPullback.iso G f g).Hom ≫ pullback.snd = G.map pullback.snd := by
simp [preserves_pullback.iso]
#align category_theory.limits.preserves_pullback.iso_hom_snd CategoryTheory.Limits.PreservesPullback.iso_hom_snd
+-/
+#print CategoryTheory.Limits.PreservesPullback.iso_inv_fst /-
@[simp, reassoc]
theorem PreservesPullback.iso_inv_fst :
(PreservesPullback.iso G f g).inv ≫ G.map pullback.fst = pullback.fst := by
simp [preserves_pullback.iso, iso.inv_comp_eq]
#align category_theory.limits.preserves_pullback.iso_inv_fst CategoryTheory.Limits.PreservesPullback.iso_inv_fst
+-/
+#print CategoryTheory.Limits.PreservesPullback.iso_inv_snd /-
@[simp, reassoc]
theorem PreservesPullback.iso_inv_snd :
(PreservesPullback.iso G f g).inv ≫ G.map pullback.snd = pullback.snd := by
simp [preserves_pullback.iso, iso.inv_comp_eq]
#align category_theory.limits.preserves_pullback.iso_inv_snd CategoryTheory.Limits.PreservesPullback.iso_inv_snd
+-/
end Pullback
@@ -153,6 +173,7 @@ variable (G : C ⥤ D)
variable {W X Y Z : C} {h : X ⟶ Z} {k : Y ⟶ Z} {f : W ⟶ X} {g : W ⟶ Y} (comm : f ≫ h = g ≫ k)
+#print CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquiv /-
/-- The map of a pushout cocone is a colimit iff the cofork consisting of the mapped morphisms is a
colimit. This essentially lets us commute `pushout_cocone.mk` with `functor.map_cocone`. -/
def isColimitMapCoconePushoutCoconeEquiv :
@@ -166,29 +187,36 @@ def isColimitMapCoconePushoutCoconeEquiv :
rintro (_ | _ | _) <;> dsimp <;>
simp only [category.comp_id, category.id_comp, ← G.map_comp]
#align category_theory.limits.is_colimit_map_cocone_pushout_cocone_equiv CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquiv
+-/
+#print CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimit /-
/-- The property of preserving pushouts expressed in terms of binary cofans. -/
def isColimitPushoutCoconeMapOfIsColimit [PreservesColimit (span f g) G]
(l : IsColimit (PushoutCocone.mk h k comm)) :
IsColimit (PushoutCocone.mk (G.map h) (G.map k) _) :=
isColimitMapCoconePushoutCoconeEquiv G comm (PreservesColimit.preserves l)
#align category_theory.limits.is_colimit_pushout_cocone_map_of_is_colimit CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimit
+-/
+#print CategoryTheory.Limits.isColimitOfIsColimitPushoutCoconeMap /-
/-- The property of reflecting pushouts expressed in terms of binary cofans. -/
def isColimitOfIsColimitPushoutCoconeMap [ReflectsColimit (span f g) G]
(l : IsColimit (PushoutCocone.mk (G.map h) (G.map k) _)) :
IsColimit (PushoutCocone.mk h k comm) :=
ReflectsColimit.reflects ((isColimitMapCoconePushoutCoconeEquiv G comm).symm l)
#align category_theory.limits.is_colimit_of_is_colimit_pushout_cocone_map CategoryTheory.Limits.isColimitOfIsColimitPushoutCoconeMap
+-/
variable (f g) [PreservesColimit (span f g) G]
+#print CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimit /-
/-- If `G` preserves pushouts and `C` has them, then the pushout cocone constructed of the mapped
morphisms of the pushout cocone is a colimit. -/
def isColimitOfHasPushoutOfPreservesColimit [HasPushout f g] :
IsColimit (PushoutCocone.mk (G.map pushout.inl) (G.map pushout.inr) _) :=
isColimitPushoutCoconeMapOfIsColimit G _ (pushoutIsPushout f g)
#align category_theory.limits.is_colimit_of_has_pushout_of_preserves_colimit CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimit
+-/
#print CategoryTheory.Limits.preservesPushoutSymmetry /-
/-- If `F` preserves the pushout of `f, g`, it also preserves the pushout of `g, f`. -/
@@ -208,42 +236,54 @@ def preservesPushoutSymmetry : PreservesColimit (span g f) G
#align category_theory.limits.preserves_pushout_symmetry CategoryTheory.Limits.preservesPushoutSymmetry
-/
+#print CategoryTheory.Limits.hasPushout_of_preservesPushout /-
theorem hasPushout_of_preservesPushout [HasPushout f g] : HasPushout (G.map f) (G.map g) :=
⟨⟨⟨_, isColimitPushoutCoconeMapOfIsColimit G _ (pushoutIsPushout _ _)⟩⟩⟩
#align category_theory.limits.has_pushout_of_preserves_pushout CategoryTheory.Limits.hasPushout_of_preservesPushout
+-/
variable [HasPushout f g] [HasPushout (G.map f) (G.map g)]
+#print CategoryTheory.Limits.PreservesPushout.iso /-
/-- If `G` preserves the pushout of `(f,g)`, then the pushout comparison map for `G` at `(f,g)` is
an isomorphism. -/
def PreservesPushout.iso : pushout (G.map f) (G.map g) ≅ G.obj (pushout f g) :=
IsColimit.coconePointUniqueUpToIso (colimit.isColimit _)
(isColimitOfHasPushoutOfPreservesColimit G f g)
#align category_theory.limits.preserves_pushout.iso CategoryTheory.Limits.PreservesPushout.iso
+-/
+#print CategoryTheory.Limits.PreservesPushout.inl_iso_hom /-
@[reassoc]
theorem PreservesPushout.inl_iso_hom :
pushout.inl ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inl := by
delta preserves_pushout.iso; simp
#align category_theory.limits.preserves_pushout.inl_iso_hom CategoryTheory.Limits.PreservesPushout.inl_iso_hom
+-/
+#print CategoryTheory.Limits.PreservesPushout.inr_iso_hom /-
@[reassoc]
theorem PreservesPushout.inr_iso_hom :
pushout.inr ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inr := by
delta preserves_pushout.iso; simp
#align category_theory.limits.preserves_pushout.inr_iso_hom CategoryTheory.Limits.PreservesPushout.inr_iso_hom
+-/
+#print CategoryTheory.Limits.PreservesPushout.inl_iso_inv /-
@[simp, reassoc]
theorem PreservesPushout.inl_iso_inv :
G.map pushout.inl ≫ (PreservesPushout.iso G f g).inv = pushout.inl := by
simp [preserves_pushout.iso, iso.comp_inv_eq]
#align category_theory.limits.preserves_pushout.inl_iso_inv CategoryTheory.Limits.PreservesPushout.inl_iso_inv
+-/
+#print CategoryTheory.Limits.PreservesPushout.inr_iso_inv /-
@[simp, reassoc]
theorem PreservesPushout.inr_iso_inv :
G.map pushout.inr ≫ (PreservesPushout.iso G f g).inv = pushout.inr := by
simp [preserves_pushout.iso, iso.comp_inv_eq]
#align category_theory.limits.preserves_pushout.inr_iso_inv CategoryTheory.Limits.PreservesPushout.inr_iso_inv
+-/
end Pushout
@@ -261,6 +301,7 @@ variable {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z}
variable [HasPullback f g] [HasPullback (G.map f) (G.map g)]
+#print CategoryTheory.Limits.PreservesPullback.ofIsoComparison /-
/-- If the pullback comparison map for `G` at `(f,g)` is an isomorphism, then `G` preserves the
pullback of `(f,g)`. -/
def PreservesPullback.ofIsoComparison [i : IsIso (pullbackComparison G f g)] :
@@ -271,13 +312,16 @@ def PreservesPullback.ofIsoComparison [i : IsIso (pullbackComparison G f g)] :
apply is_limit.of_point_iso (limit.is_limit (cospan (G.map f) (G.map g)))
apply i
#align category_theory.limits.preserves_pullback.of_iso_comparison CategoryTheory.Limits.PreservesPullback.ofIsoComparison
+-/
variable [PreservesLimit (cospan f g) G]
+#print CategoryTheory.Limits.PreservesPullback.iso_hom /-
@[simp]
theorem PreservesPullback.iso_hom : (PreservesPullback.iso G f g).Hom = pullbackComparison G f g :=
rfl
#align category_theory.limits.preserves_pullback.iso_hom CategoryTheory.Limits.PreservesPullback.iso_hom
+-/
instance : IsIso (pullbackComparison G f g) :=
by
@@ -292,6 +336,7 @@ variable {X Y Z : C} {f : X ⟶ Y} {g : X ⟶ Z}
variable [HasPushout f g] [HasPushout (G.map f) (G.map g)]
+#print CategoryTheory.Limits.PreservesPushout.ofIsoComparison /-
/-- If the pushout comparison map for `G` at `(f,g)` is an isomorphism, then `G` preserves the
pushout of `(f,g)`. -/
def PreservesPushout.ofIsoComparison [i : IsIso (pushoutComparison G f g)] :
@@ -302,13 +347,16 @@ def PreservesPushout.ofIsoComparison [i : IsIso (pushoutComparison G f g)] :
apply is_colimit.of_point_iso (colimit.is_colimit (span (G.map f) (G.map g)))
apply i
#align category_theory.limits.preserves_pushout.of_iso_comparison CategoryTheory.Limits.PreservesPushout.ofIsoComparison
+-/
variable [PreservesColimit (span f g) G]
+#print CategoryTheory.Limits.PreservesPushout.iso_hom /-
@[simp]
theorem PreservesPushout.iso_hom : (PreservesPushout.iso G f g).Hom = pushoutComparison G f g :=
rfl
#align category_theory.limits.preserves_pushout.iso_hom CategoryTheory.Limits.PreservesPushout.iso_hom
+-/
instance : IsIso (pushoutComparison G f g) :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -50,9 +50,6 @@ variable (G : C ⥤ D)
variable {W X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z} {h : W ⟶ X} {k : W ⟶ Y} (comm : h ≫ f = k ≫ g)
-/- warning: category_theory.limits.is_limit_map_cone_pullback_cone_equiv -> CategoryTheory.Limits.isLimitMapConePullbackConeEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_map_cone_pullback_cone_equiv CategoryTheory.Limits.isLimitMapConePullbackConeEquivₓ'. -/
/-- The map of a pullback cone is a limit iff the fork consisting of the mapped morphisms is a
limit. This essentially lets us commute `pullback_cone.mk` with `functor.map_cone`. -/
def isLimitMapConePullbackConeEquiv :
@@ -66,18 +63,12 @@ def isLimitMapConePullbackConeEquiv :
rintro (_ | _ | _) <;> dsimp <;> simp only [comp_id, id_comp, G.map_comp]
#align category_theory.limits.is_limit_map_cone_pullback_cone_equiv CategoryTheory.Limits.isLimitMapConePullbackConeEquiv
-/- warning: category_theory.limits.is_limit_pullback_cone_map_of_is_limit -> CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_pullback_cone_map_of_is_limit CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimitₓ'. -/
/-- The property of preserving pullbacks expressed in terms of binary fans. -/
def isLimitPullbackConeMapOfIsLimit [PreservesLimit (cospan f g) G]
(l : IsLimit (PullbackCone.mk h k comm)) : IsLimit (PullbackCone.mk (G.map h) (G.map k) _) :=
isLimitMapConePullbackConeEquiv G comm (PreservesLimit.preserves l)
#align category_theory.limits.is_limit_pullback_cone_map_of_is_limit CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimit
-/- warning: category_theory.limits.is_limit_of_is_limit_pullback_cone_map -> CategoryTheory.Limits.isLimitOfIsLimitPullbackConeMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_of_is_limit_pullback_cone_map CategoryTheory.Limits.isLimitOfIsLimitPullbackConeMapₓ'. -/
/-- The property of reflecting pullbacks expressed in terms of binary fans. -/
def isLimitOfIsLimitPullbackConeMap [ReflectsLimit (cospan f g) G]
(l : IsLimit (PullbackCone.mk (G.map h) (G.map k) _)) : IsLimit (PullbackCone.mk h k comm) :=
@@ -86,9 +77,6 @@ def isLimitOfIsLimitPullbackConeMap [ReflectsLimit (cospan f g) G]
variable (f g) [PreservesLimit (cospan f g) G]
-/- warning: category_theory.limits.is_limit_of_has_pullback_of_preserves_limit -> CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_of_has_pullback_of_preserves_limit CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimitₓ'. -/
/-- If `G` preserves pullbacks and `C` has them, then the pullback cone constructed of the mapped
morphisms of the pullback cone is a limit. -/
def isLimitOfHasPullbackOfPreservesLimit [HasPullback f g] :
@@ -117,60 +105,36 @@ def preservesPullbackSymmetry : PreservesLimit (cospan g f) G
#align category_theory.limits.preserves_pullback_symmetry CategoryTheory.Limits.preservesPullbackSymmetry
-/
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theorem hasPullback_of_preservesPullback [HasPullback f g] : HasPullback (G.map f) (G.map g) :=
⟨⟨⟨_, isLimitPullbackConeMapOfIsLimit G _ (pullbackIsPullback _ _)⟩⟩⟩
#align category_theory.limits.has_pullback_of_preserves_pullback CategoryTheory.Limits.hasPullback_of_preservesPullback
variable [HasPullback f g] [HasPullback (G.map f) (G.map g)]
-/- warning: category_theory.limits.preserves_pullback.iso -> CategoryTheory.Limits.PreservesPullback.iso is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso CategoryTheory.Limits.PreservesPullback.isoₓ'. -/
/-- If `G` preserves the pullback of `(f,g)`, then the pullback comparison map for `G` at `(f,g)` is
an isomorphism. -/
def PreservesPullback.iso : G.obj (pullback f g) ≅ pullback (G.map f) (G.map g) :=
IsLimit.conePointUniqueUpToIso (isLimitOfHasPullbackOfPreservesLimit G f g) (limit.isLimit _)
#align category_theory.limits.preserves_pullback.iso CategoryTheory.Limits.PreservesPullback.iso
-/- warning: category_theory.limits.preserves_pullback.iso_hom_fst -> CategoryTheory.Limits.PreservesPullback.iso_hom_fst is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_hom_fst CategoryTheory.Limits.PreservesPullback.iso_hom_fstₓ'. -/
@[reassoc]
theorem PreservesPullback.iso_hom_fst :
(PreservesPullback.iso G f g).Hom ≫ pullback.fst = G.map pullback.fst := by
simp [preserves_pullback.iso]
#align category_theory.limits.preserves_pullback.iso_hom_fst CategoryTheory.Limits.PreservesPullback.iso_hom_fst
-/- warning: category_theory.limits.preserves_pullback.iso_hom_snd -> CategoryTheory.Limits.PreservesPullback.iso_hom_snd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_hom_snd CategoryTheory.Limits.PreservesPullback.iso_hom_sndₓ'. -/
@[reassoc]
theorem PreservesPullback.iso_hom_snd :
(PreservesPullback.iso G f g).Hom ≫ pullback.snd = G.map pullback.snd := by
simp [preserves_pullback.iso]
#align category_theory.limits.preserves_pullback.iso_hom_snd CategoryTheory.Limits.PreservesPullback.iso_hom_snd
-/- warning: category_theory.limits.preserves_pullback.iso_inv_fst -> CategoryTheory.Limits.PreservesPullback.iso_inv_fst is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_inv_fst CategoryTheory.Limits.PreservesPullback.iso_inv_fstₓ'. -/
@[simp, reassoc]
theorem PreservesPullback.iso_inv_fst :
(PreservesPullback.iso G f g).inv ≫ G.map pullback.fst = pullback.fst := by
simp [preserves_pullback.iso, iso.inv_comp_eq]
#align category_theory.limits.preserves_pullback.iso_inv_fst CategoryTheory.Limits.PreservesPullback.iso_inv_fst
-/- warning: category_theory.limits.preserves_pullback.iso_inv_snd -> CategoryTheory.Limits.PreservesPullback.iso_inv_snd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_inv_snd CategoryTheory.Limits.PreservesPullback.iso_inv_sndₓ'. -/
@[simp, reassoc]
theorem PreservesPullback.iso_inv_snd :
(PreservesPullback.iso G f g).inv ≫ G.map pullback.snd = pullback.snd := by
@@ -189,9 +153,6 @@ variable (G : C ⥤ D)
variable {W X Y Z : C} {h : X ⟶ Z} {k : Y ⟶ Z} {f : W ⟶ X} {g : W ⟶ Y} (comm : f ≫ h = g ≫ k)
-/- warning: category_theory.limits.is_colimit_map_cocone_pushout_cocone_equiv -> CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_map_cocone_pushout_cocone_equiv CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquivₓ'. -/
/-- The map of a pushout cocone is a colimit iff the cofork consisting of the mapped morphisms is a
colimit. This essentially lets us commute `pushout_cocone.mk` with `functor.map_cocone`. -/
def isColimitMapCoconePushoutCoconeEquiv :
@@ -206,9 +167,6 @@ def isColimitMapCoconePushoutCoconeEquiv :
simp only [category.comp_id, category.id_comp, ← G.map_comp]
#align category_theory.limits.is_colimit_map_cocone_pushout_cocone_equiv CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquiv
-/- warning: category_theory.limits.is_colimit_pushout_cocone_map_of_is_colimit -> CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_pushout_cocone_map_of_is_colimit CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimitₓ'. -/
/-- The property of preserving pushouts expressed in terms of binary cofans. -/
def isColimitPushoutCoconeMapOfIsColimit [PreservesColimit (span f g) G]
(l : IsColimit (PushoutCocone.mk h k comm)) :
@@ -216,9 +174,6 @@ def isColimitPushoutCoconeMapOfIsColimit [PreservesColimit (span f g) G]
isColimitMapCoconePushoutCoconeEquiv G comm (PreservesColimit.preserves l)
#align category_theory.limits.is_colimit_pushout_cocone_map_of_is_colimit CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimit
-/- warning: category_theory.limits.is_colimit_of_is_colimit_pushout_cocone_map -> CategoryTheory.Limits.isColimitOfIsColimitPushoutCoconeMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_of_is_colimit_pushout_cocone_map CategoryTheory.Limits.isColimitOfIsColimitPushoutCoconeMapₓ'. -/
/-- The property of reflecting pushouts expressed in terms of binary cofans. -/
def isColimitOfIsColimitPushoutCoconeMap [ReflectsColimit (span f g) G]
(l : IsColimit (PushoutCocone.mk (G.map h) (G.map k) _)) :
@@ -228,9 +183,6 @@ def isColimitOfIsColimitPushoutCoconeMap [ReflectsColimit (span f g) G]
variable (f g) [PreservesColimit (span f g) G]
-/- warning: category_theory.limits.is_colimit_of_has_pushout_of_preserves_colimit -> CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_of_has_pushout_of_preserves_colimit CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimitₓ'. -/
/-- If `G` preserves pushouts and `C` has them, then the pushout cocone constructed of the mapped
morphisms of the pushout cocone is a colimit. -/
def isColimitOfHasPushoutOfPreservesColimit [HasPushout f g] :
@@ -256,24 +208,12 @@ def preservesPushoutSymmetry : PreservesColimit (span g f) G
#align category_theory.limits.preserves_pushout_symmetry CategoryTheory.Limits.preservesPushoutSymmetry
-/
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theorem hasPushout_of_preservesPushout [HasPushout f g] : HasPushout (G.map f) (G.map g) :=
⟨⟨⟨_, isColimitPushoutCoconeMapOfIsColimit G _ (pushoutIsPushout _ _)⟩⟩⟩
#align category_theory.limits.has_pushout_of_preserves_pushout CategoryTheory.Limits.hasPushout_of_preservesPushout
variable [HasPushout f g] [HasPushout (G.map f) (G.map g)]
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-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.iso CategoryTheory.Limits.PreservesPushout.isoₓ'. -/
/-- If `G` preserves the pushout of `(f,g)`, then the pushout comparison map for `G` at `(f,g)` is
an isomorphism. -/
def PreservesPushout.iso : pushout (G.map f) (G.map g) ≅ G.obj (pushout f g) :=
@@ -281,36 +221,24 @@ def PreservesPushout.iso : pushout (G.map f) (G.map g) ≅ G.obj (pushout f g) :
(isColimitOfHasPushoutOfPreservesColimit G f g)
#align category_theory.limits.preserves_pushout.iso CategoryTheory.Limits.PreservesPushout.iso
-/- warning: category_theory.limits.preserves_pushout.inl_iso_hom -> CategoryTheory.Limits.PreservesPushout.inl_iso_hom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inl_iso_hom CategoryTheory.Limits.PreservesPushout.inl_iso_homₓ'. -/
@[reassoc]
theorem PreservesPushout.inl_iso_hom :
pushout.inl ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inl := by
delta preserves_pushout.iso; simp
#align category_theory.limits.preserves_pushout.inl_iso_hom CategoryTheory.Limits.PreservesPushout.inl_iso_hom
-/- warning: category_theory.limits.preserves_pushout.inr_iso_hom -> CategoryTheory.Limits.PreservesPushout.inr_iso_hom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inr_iso_hom CategoryTheory.Limits.PreservesPushout.inr_iso_homₓ'. -/
@[reassoc]
theorem PreservesPushout.inr_iso_hom :
pushout.inr ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inr := by
delta preserves_pushout.iso; simp
#align category_theory.limits.preserves_pushout.inr_iso_hom CategoryTheory.Limits.PreservesPushout.inr_iso_hom
-/- warning: category_theory.limits.preserves_pushout.inl_iso_inv -> CategoryTheory.Limits.PreservesPushout.inl_iso_inv is a dubious translation:
-<too large>
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@[simp, reassoc]
theorem PreservesPushout.inl_iso_inv :
G.map pushout.inl ≫ (PreservesPushout.iso G f g).inv = pushout.inl := by
simp [preserves_pushout.iso, iso.comp_inv_eq]
#align category_theory.limits.preserves_pushout.inl_iso_inv CategoryTheory.Limits.PreservesPushout.inl_iso_inv
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@[simp, reassoc]
theorem PreservesPushout.inr_iso_inv :
G.map pushout.inr ≫ (PreservesPushout.iso G f g).inv = pushout.inr := by
@@ -333,12 +261,6 @@ variable {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z}
variable [HasPullback f g] [HasPullback (G.map f) (G.map g)]
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-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.of_iso_comparison CategoryTheory.Limits.PreservesPullback.ofIsoComparisonₓ'. -/
/-- If the pullback comparison map for `G` at `(f,g)` is an isomorphism, then `G` preserves the
pullback of `(f,g)`. -/
def PreservesPullback.ofIsoComparison [i : IsIso (pullbackComparison G f g)] :
@@ -352,9 +274,6 @@ def PreservesPullback.ofIsoComparison [i : IsIso (pullbackComparison G f g)] :
variable [PreservesLimit (cospan f g) G]
-/- warning: category_theory.limits.preserves_pullback.iso_hom -> CategoryTheory.Limits.PreservesPullback.iso_hom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_hom CategoryTheory.Limits.PreservesPullback.iso_homₓ'. -/
@[simp]
theorem PreservesPullback.iso_hom : (PreservesPullback.iso G f g).Hom = pullbackComparison G f g :=
rfl
@@ -373,12 +292,6 @@ variable {X Y Z : C} {f : X ⟶ Y} {g : X ⟶ Z}
variable [HasPushout f g] [HasPushout (G.map f) (G.map g)]
-/- warning: category_theory.limits.preserves_pushout.of_iso_comparison -> CategoryTheory.Limits.PreservesPushout.ofIsoComparison is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.of_iso_comparison CategoryTheory.Limits.PreservesPushout.ofIsoComparisonₓ'. -/
/-- If the pushout comparison map for `G` at `(f,g)` is an isomorphism, then `G` preserves the
pushout of `(f,g)`. -/
def PreservesPushout.ofIsoComparison [i : IsIso (pushoutComparison G f g)] :
@@ -392,9 +305,6 @@ def PreservesPushout.ofIsoComparison [i : IsIso (pushoutComparison G f g)] :
variable [PreservesColimit (span f g) G]
-/- warning: category_theory.limits.preserves_pushout.iso_hom -> CategoryTheory.Limits.PreservesPushout.iso_hom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.iso_hom CategoryTheory.Limits.PreservesPushout.iso_homₓ'. -/
@[simp]
theorem PreservesPushout.iso_hom : (PreservesPushout.iso G f g).Hom = pushoutComparison G f g :=
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -106,8 +106,7 @@ def preservesPullbackSymmetry : PreservesLimit (cospan g f) G
apply pullback_cone.flip_is_limit
apply (is_limit_map_cone_pullback_cone_equiv _ _).toFun
· apply (config := { instances := false }) preserves_limit.preserves
- · dsimp
- infer_instance
+ · dsimp; infer_instance
apply pullback_cone.flip_is_limit
apply is_limit.of_iso_limit _ (pullback_cone.iso_mk _)
exact (is_limit.postcompose_hom_equiv (diagramIsoCospan.{v₁} _) _).invFun hc
@@ -249,8 +248,7 @@ def preservesPushoutSymmetry : PreservesColimit (span g f) G
apply pushout_cocone.flip_is_colimit
apply (is_colimit_map_cocone_pushout_cocone_equiv _ _).toFun
· apply (config := { instances := false }) preserves_colimit.preserves
- · dsimp
- infer_instance
+ · dsimp; infer_instance
apply pushout_cocone.flip_is_colimit
apply is_colimit.of_iso_colimit _ (pushout_cocone.iso_mk _)
exact (is_colimit.precompose_hom_equiv (diagramIsoSpan.{v₁} _) _).invFun hc
@@ -288,10 +286,8 @@ def PreservesPushout.iso : pushout (G.map f) (G.map g) ≅ G.obj (pushout f g) :
Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inl_iso_hom CategoryTheory.Limits.PreservesPushout.inl_iso_homₓ'. -/
@[reassoc]
theorem PreservesPushout.inl_iso_hom :
- pushout.inl ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inl :=
- by
- delta preserves_pushout.iso
- simp
+ pushout.inl ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inl := by
+ delta preserves_pushout.iso; simp
#align category_theory.limits.preserves_pushout.inl_iso_hom CategoryTheory.Limits.PreservesPushout.inl_iso_hom
/- warning: category_theory.limits.preserves_pushout.inr_iso_hom -> CategoryTheory.Limits.PreservesPushout.inr_iso_hom is a dubious translation:
@@ -299,10 +295,8 @@ theorem PreservesPushout.inl_iso_hom :
Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inr_iso_hom CategoryTheory.Limits.PreservesPushout.inr_iso_homₓ'. -/
@[reassoc]
theorem PreservesPushout.inr_iso_hom :
- pushout.inr ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inr :=
- by
- delta preserves_pushout.iso
- simp
+ pushout.inr ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inr := by
+ delta preserves_pushout.iso; simp
#align category_theory.limits.preserves_pushout.inr_iso_hom CategoryTheory.Limits.PreservesPushout.inr_iso_hom
/- warning: category_theory.limits.preserves_pushout.inl_iso_inv -> CategoryTheory.Limits.PreservesPushout.inl_iso_inv is a dubious translation:
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -51,10 +51,7 @@ variable (G : C ⥤ D)
variable {W X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z} {h : W ⟶ X} {k : W ⟶ Y} (comm : h ≫ f = k ≫ g)
/- warning: category_theory.limits.is_limit_map_cone_pullback_cone_equiv -> CategoryTheory.Limits.isLimitMapConePullbackConeEquiv is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_map_cone_pullback_cone_equiv CategoryTheory.Limits.isLimitMapConePullbackConeEquivₓ'. -/
/-- The map of a pullback cone is a limit iff the fork consisting of the mapped morphisms is a
limit. This essentially lets us commute `pullback_cone.mk` with `functor.map_cone`. -/
@@ -70,10 +67,7 @@ def isLimitMapConePullbackConeEquiv :
#align category_theory.limits.is_limit_map_cone_pullback_cone_equiv CategoryTheory.Limits.isLimitMapConePullbackConeEquiv
/- warning: category_theory.limits.is_limit_pullback_cone_map_of_is_limit -> CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimit is a dubious translation:
-lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_pullback_cone_map_of_is_limit CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimitₓ'. -/
/-- The property of preserving pullbacks expressed in terms of binary fans. -/
def isLimitPullbackConeMapOfIsLimit [PreservesLimit (cospan f g) G]
@@ -82,10 +76,7 @@ def isLimitPullbackConeMapOfIsLimit [PreservesLimit (cospan f g) G]
#align category_theory.limits.is_limit_pullback_cone_map_of_is_limit CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimit
/- warning: category_theory.limits.is_limit_of_is_limit_pullback_cone_map -> CategoryTheory.Limits.isLimitOfIsLimitPullbackConeMap is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_of_is_limit_pullback_cone_map CategoryTheory.Limits.isLimitOfIsLimitPullbackConeMapₓ'. -/
/-- The property of reflecting pullbacks expressed in terms of binary fans. -/
def isLimitOfIsLimitPullbackConeMap [ReflectsLimit (cospan f g) G]
@@ -96,10 +87,7 @@ def isLimitOfIsLimitPullbackConeMap [ReflectsLimit (cospan f g) G]
variable (f g) [PreservesLimit (cospan f g) G]
/- warning: category_theory.limits.is_limit_of_has_pullback_of_preserves_limit -> CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimit is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_of_has_pullback_of_preserves_limit CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimitₓ'. -/
/-- If `G` preserves pullbacks and `C` has them, then the pullback cone constructed of the mapped
morphisms of the pullback cone is a limit. -/
@@ -155,10 +143,7 @@ def PreservesPullback.iso : G.obj (pullback f g) ≅ pullback (G.map f) (G.map g
#align category_theory.limits.preserves_pullback.iso CategoryTheory.Limits.PreservesPullback.iso
/- warning: category_theory.limits.preserves_pullback.iso_hom_fst -> CategoryTheory.Limits.PreservesPullback.iso_hom_fst is a dubious translation:
-lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_hom_fst CategoryTheory.Limits.PreservesPullback.iso_hom_fstₓ'. -/
@[reassoc]
theorem PreservesPullback.iso_hom_fst :
@@ -167,10 +152,7 @@ theorem PreservesPullback.iso_hom_fst :
#align category_theory.limits.preserves_pullback.iso_hom_fst CategoryTheory.Limits.PreservesPullback.iso_hom_fst
/- warning: category_theory.limits.preserves_pullback.iso_hom_snd -> CategoryTheory.Limits.PreservesPullback.iso_hom_snd is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_hom_snd CategoryTheory.Limits.PreservesPullback.iso_hom_sndₓ'. -/
@[reassoc]
theorem PreservesPullback.iso_hom_snd :
@@ -179,10 +161,7 @@ theorem PreservesPullback.iso_hom_snd :
#align category_theory.limits.preserves_pullback.iso_hom_snd CategoryTheory.Limits.PreservesPullback.iso_hom_snd
/- warning: category_theory.limits.preserves_pullback.iso_inv_fst -> CategoryTheory.Limits.PreservesPullback.iso_inv_fst is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_inv_fst CategoryTheory.Limits.PreservesPullback.iso_inv_fstₓ'. -/
@[simp, reassoc]
theorem PreservesPullback.iso_inv_fst :
@@ -191,10 +170,7 @@ theorem PreservesPullback.iso_inv_fst :
#align category_theory.limits.preserves_pullback.iso_inv_fst CategoryTheory.Limits.PreservesPullback.iso_inv_fst
/- warning: category_theory.limits.preserves_pullback.iso_inv_snd -> CategoryTheory.Limits.PreservesPullback.iso_inv_snd is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_inv_snd CategoryTheory.Limits.PreservesPullback.iso_inv_sndₓ'. -/
@[simp, reassoc]
theorem PreservesPullback.iso_inv_snd :
@@ -215,10 +191,7 @@ variable (G : C ⥤ D)
variable {W X Y Z : C} {h : X ⟶ Z} {k : Y ⟶ Z} {f : W ⟶ X} {g : W ⟶ Y} (comm : f ≫ h = g ≫ k)
/- warning: category_theory.limits.is_colimit_map_cocone_pushout_cocone_equiv -> CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquiv is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_map_cocone_pushout_cocone_equiv CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquivₓ'. -/
/-- The map of a pushout cocone is a colimit iff the cofork consisting of the mapped morphisms is a
colimit. This essentially lets us commute `pushout_cocone.mk` with `functor.map_cocone`. -/
@@ -235,10 +208,7 @@ def isColimitMapCoconePushoutCoconeEquiv :
#align category_theory.limits.is_colimit_map_cocone_pushout_cocone_equiv CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquiv
/- warning: category_theory.limits.is_colimit_pushout_cocone_map_of_is_colimit -> CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimit is a dubious translation:
-lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_pushout_cocone_map_of_is_colimit CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimitₓ'. -/
/-- The property of preserving pushouts expressed in terms of binary cofans. -/
def isColimitPushoutCoconeMapOfIsColimit [PreservesColimit (span f g) G]
@@ -248,10 +218,7 @@ def isColimitPushoutCoconeMapOfIsColimit [PreservesColimit (span f g) G]
#align category_theory.limits.is_colimit_pushout_cocone_map_of_is_colimit CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimit
/- warning: category_theory.limits.is_colimit_of_is_colimit_pushout_cocone_map -> CategoryTheory.Limits.isColimitOfIsColimitPushoutCoconeMap is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_of_is_colimit_pushout_cocone_map CategoryTheory.Limits.isColimitOfIsColimitPushoutCoconeMapₓ'. -/
/-- The property of reflecting pushouts expressed in terms of binary cofans. -/
def isColimitOfIsColimitPushoutCoconeMap [ReflectsColimit (span f g) G]
@@ -263,10 +230,7 @@ def isColimitOfIsColimitPushoutCoconeMap [ReflectsColimit (span f g) G]
variable (f g) [PreservesColimit (span f g) G]
/- warning: category_theory.limits.is_colimit_of_has_pushout_of_preserves_colimit -> CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimit is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_of_has_pushout_of_preserves_colimit CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimitₓ'. -/
/-- If `G` preserves pushouts and `C` has them, then the pushout cocone constructed of the mapped
morphisms of the pushout cocone is a colimit. -/
@@ -320,10 +284,7 @@ def PreservesPushout.iso : pushout (G.map f) (G.map g) ≅ G.obj (pushout f g) :
#align category_theory.limits.preserves_pushout.iso CategoryTheory.Limits.PreservesPushout.iso
/- warning: category_theory.limits.preserves_pushout.inl_iso_hom -> CategoryTheory.Limits.PreservesPushout.inl_iso_hom is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inl_iso_hom CategoryTheory.Limits.PreservesPushout.inl_iso_homₓ'. -/
@[reassoc]
theorem PreservesPushout.inl_iso_hom :
@@ -334,10 +295,7 @@ theorem PreservesPushout.inl_iso_hom :
#align category_theory.limits.preserves_pushout.inl_iso_hom CategoryTheory.Limits.PreservesPushout.inl_iso_hom
/- warning: category_theory.limits.preserves_pushout.inr_iso_hom -> CategoryTheory.Limits.PreservesPushout.inr_iso_hom is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inr_iso_hom CategoryTheory.Limits.PreservesPushout.inr_iso_homₓ'. -/
@[reassoc]
theorem PreservesPushout.inr_iso_hom :
@@ -348,10 +306,7 @@ theorem PreservesPushout.inr_iso_hom :
#align category_theory.limits.preserves_pushout.inr_iso_hom CategoryTheory.Limits.PreservesPushout.inr_iso_hom
/- warning: category_theory.limits.preserves_pushout.inl_iso_inv -> CategoryTheory.Limits.PreservesPushout.inl_iso_inv is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inl_iso_inv CategoryTheory.Limits.PreservesPushout.inl_iso_invₓ'. -/
@[simp, reassoc]
theorem PreservesPushout.inl_iso_inv :
@@ -360,10 +315,7 @@ theorem PreservesPushout.inl_iso_inv :
#align category_theory.limits.preserves_pushout.inl_iso_inv CategoryTheory.Limits.PreservesPushout.inl_iso_inv
/- warning: category_theory.limits.preserves_pushout.inr_iso_inv -> CategoryTheory.Limits.PreservesPushout.inr_iso_inv is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inr_iso_inv CategoryTheory.Limits.PreservesPushout.inr_iso_invₓ'. -/
@[simp, reassoc]
theorem PreservesPushout.inr_iso_inv :
@@ -407,10 +359,7 @@ def PreservesPullback.ofIsoComparison [i : IsIso (pullbackComparison G f g)] :
variable [PreservesLimit (cospan f g) G]
/- warning: category_theory.limits.preserves_pullback.iso_hom -> CategoryTheory.Limits.PreservesPullback.iso_hom is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_hom CategoryTheory.Limits.PreservesPullback.iso_homₓ'. -/
@[simp]
theorem PreservesPullback.iso_hom : (PreservesPullback.iso G f g).Hom = pullbackComparison G f g :=
@@ -450,10 +399,7 @@ def PreservesPushout.ofIsoComparison [i : IsIso (pushoutComparison G f g)] :
variable [PreservesColimit (span f g) G]
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_inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Y f) (Prefunctor.map.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Z g)] [_inst_5 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u1, u2, u3} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u2} C _inst_1 X Y Z f g) G], Eq.{succ u1} (Quiver.Hom.{succ u1, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Limits.pushout.{u1, u3} D _inst_2 (Prefunctor.obj.{succ u1, succ u1, u2, u3} C 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_inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Y f) (Prefunctor.map.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Z g) _inst_4) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pushout.{u1, u2} C _inst_1 X Y Z f g _inst_3))) (CategoryTheory.Iso.hom.{u1, u3} D _inst_2 (CategoryTheory.Limits.pushout.{u1, u3} D _inst_2 (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Y f) (Prefunctor.map.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Z g) _inst_4) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pushout.{u1, u2} C _inst_1 X Y Z f g _inst_3)) (CategoryTheory.Limits.PreservesPushout.iso.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X Y Z f g _inst_5 _inst_3 _inst_4)) (CategoryTheory.Limits.pushoutComparison.{u1, u1, u2, u3} C _inst_1 D _inst_2 X Y Z G f g _inst_3 _inst_4)
+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.iso_hom CategoryTheory.Limits.PreservesPushout.iso_homₓ'. -/
@[simp]
theorem PreservesPushout.iso_hom : (PreservesPushout.iso G f g).Hom = pushoutComparison G f g :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -160,7 +160,7 @@ lean 3 declaration is
but is expected to have type
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Z) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y Z) [_inst_3 : CategoryTheory.Limits.PreservesLimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingCospan (CategoryTheory.Limits.WidePullbackShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.cospan.{u1, u3} C _inst_1 X Y Z f g) G] [_inst_4 : CategoryTheory.Limits.HasPullback.{u1, u3} C _inst_1 X Y Z f g] [_inst_5 : CategoryTheory.Limits.HasPullback.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Z f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g)], Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pullback.{u1, u3} C _inst_1 X Y Z f g _inst_4)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X)) (CategoryTheory.CategoryStruct.comp.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pullback.{u1, u3} C _inst_1 X Y Z f g _inst_4)) (CategoryTheory.Limits.pullback.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Z f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g) _inst_5) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (CategoryTheory.Iso.hom.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pullback.{u1, u3} C _inst_1 X Y Z f g _inst_4)) (CategoryTheory.Limits.pullback.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, 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u4} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Z f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g) _inst_5) (CategoryTheory.Limits.PreservesPullback.iso.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X Y Z f g _inst_3 _inst_4 _inst_5)) (CategoryTheory.Limits.pullback.fst.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Z f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g) _inst_5)) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pullback.{u1, u3} C _inst_1 X Y Z f g _inst_4) X (CategoryTheory.Limits.pullback.fst.{u1, u3} C _inst_1 X Y Z f g _inst_4))
Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_hom_fst CategoryTheory.Limits.PreservesPullback.iso_hom_fstₓ'. -/
-@[reassoc.1]
+@[reassoc]
theorem PreservesPullback.iso_hom_fst :
(PreservesPullback.iso G f g).Hom ≫ pullback.fst = G.map pullback.fst := by
simp [preserves_pullback.iso]
@@ -172,7 +172,7 @@ lean 3 declaration is
but is expected to have type
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Z) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y Z) [_inst_3 : CategoryTheory.Limits.PreservesLimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingCospan (CategoryTheory.Limits.WidePullbackShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.cospan.{u1, u3} C _inst_1 X Y Z f g) G] [_inst_4 : CategoryTheory.Limits.HasPullback.{u1, u3} C _inst_1 X Y Z f g] [_inst_5 : CategoryTheory.Limits.HasPullback.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Z f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g)], Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C 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u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pullback.{u1, u3} C _inst_1 X Y Z f g _inst_4)) (CategoryTheory.Limits.pullback.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ 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(CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g) _inst_5) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (CategoryTheory.Iso.hom.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pullback.{u1, u3} C _inst_1 X Y Z f g _inst_4)) (CategoryTheory.Limits.pullback.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, 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u4} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Z f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g) _inst_5) (CategoryTheory.Limits.PreservesPullback.iso.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X Y Z f g _inst_3 _inst_4 _inst_5)) (CategoryTheory.Limits.pullback.snd.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Z f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g) _inst_5)) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pullback.{u1, u3} C _inst_1 X Y Z f g _inst_4) Y (CategoryTheory.Limits.pullback.snd.{u1, u3} C _inst_1 X Y Z f g _inst_4))
Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_hom_snd CategoryTheory.Limits.PreservesPullback.iso_hom_sndₓ'. -/
-@[reassoc.1]
+@[reassoc]
theorem PreservesPullback.iso_hom_snd :
(PreservesPullback.iso G f g).Hom ≫ pullback.snd = G.map pullback.snd := by
simp [preserves_pullback.iso]
@@ -184,7 +184,7 @@ lean 3 declaration is
but is expected to have type
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Z) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y Z) [_inst_3 : CategoryTheory.Limits.PreservesLimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingCospan (CategoryTheory.Limits.WidePullbackShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.cospan.{u1, u3} C _inst_1 X Y Z f g) G] [_inst_4 : CategoryTheory.Limits.HasPullback.{u1, u3} C _inst_1 X Y Z f g] [_inst_5 : CategoryTheory.Limits.HasPullback.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Z f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g)], Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Limits.pullback.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C 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Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_inv_fst CategoryTheory.Limits.PreservesPullback.iso_inv_fstₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem PreservesPullback.iso_inv_fst :
(PreservesPullback.iso G f g).inv ≫ G.map pullback.fst = pullback.fst := by
simp [preserves_pullback.iso, iso.inv_comp_eq]
@@ -196,7 +196,7 @@ lean 3 declaration is
but is expected to have type
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Z) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y Z) [_inst_3 : CategoryTheory.Limits.PreservesLimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingCospan (CategoryTheory.Limits.WidePullbackShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.cospan.{u1, u3} C _inst_1 X Y Z f g) G] [_inst_4 : CategoryTheory.Limits.HasPullback.{u1, u3} C _inst_1 X Y Z f g] [_inst_5 : CategoryTheory.Limits.HasPullback.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C 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u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g) _inst_5) (CategoryTheory.Limits.PreservesPullback.iso.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X Y Z f g _inst_3 _inst_4 _inst_5)) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pullback.{u1, u3} C _inst_1 X Y Z f g _inst_4) Y (CategoryTheory.Limits.pullback.snd.{u1, u3} C _inst_1 X Y Z f g _inst_4))) (CategoryTheory.Limits.pullback.snd.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Z f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g) _inst_5)
Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_inv_snd CategoryTheory.Limits.PreservesPullback.iso_inv_sndₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem PreservesPullback.iso_inv_snd :
(PreservesPullback.iso G f g).inv ≫ G.map pullback.snd = pullback.snd := by
simp [preserves_pullback.iso, iso.inv_comp_eq]
@@ -325,7 +325,7 @@ lean 3 declaration is
but is expected to have type
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g] [_inst_5 : CategoryTheory.Limits.HasPushout.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W X f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W Y g)], Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pushout.{u1, u3} C _inst_1 W X Y f g _inst_4))) (CategoryTheory.CategoryStruct.comp.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (CategoryTheory.Limits.pushout.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W X f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W Y g) _inst_5) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pushout.{u1, u3} C _inst_1 W X Y f g _inst_4)) (CategoryTheory.Limits.pushout.inl.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W X f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W Y g) _inst_5) (CategoryTheory.Iso.hom.{u2, u4} D _inst_2 (CategoryTheory.Limits.pushout.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W X f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W Y g) _inst_5) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pushout.{u1, u3} C _inst_1 W X Y f g _inst_4)) (CategoryTheory.Limits.PreservesPushout.iso.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W X Y f g _inst_3 _inst_4 _inst_5))) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X (CategoryTheory.Limits.pushout.{u1, u3} C _inst_1 W X Y f g _inst_4) (CategoryTheory.Limits.pushout.inl.{u1, u3} C _inst_1 W X Y f g _inst_4))
Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inl_iso_hom CategoryTheory.Limits.PreservesPushout.inl_iso_homₓ'. -/
-@[reassoc.1]
+@[reassoc]
theorem PreservesPushout.inl_iso_hom :
pushout.inl ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inl :=
by
@@ -339,7 +339,7 @@ lean 3 declaration is
but is expected to have type
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g] [_inst_5 : CategoryTheory.Limits.HasPushout.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W X f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W Y g)], Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C 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u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W Y g) _inst_5) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pushout.{u1, u3} C _inst_1 W X Y f g _inst_4)) (CategoryTheory.Limits.PreservesPushout.iso.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W X Y f g _inst_3 _inst_4 _inst_5))) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y (CategoryTheory.Limits.pushout.{u1, u3} C _inst_1 W X Y f g _inst_4) (CategoryTheory.Limits.pushout.inr.{u1, u3} C _inst_1 W X Y f g _inst_4))
Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inr_iso_hom CategoryTheory.Limits.PreservesPushout.inr_iso_homₓ'. -/
-@[reassoc.1]
+@[reassoc]
theorem PreservesPushout.inr_iso_hom :
pushout.inr ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inr :=
by
@@ -353,7 +353,7 @@ lean 3 declaration is
but is expected to have type
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g] [_inst_5 : CategoryTheory.Limits.HasPushout.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C 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_inst_1 D _inst_2 G) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W X f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W Y g)], Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C 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Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inl_iso_inv CategoryTheory.Limits.PreservesPushout.inl_iso_invₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem PreservesPushout.inl_iso_inv :
G.map pushout.inl ≫ (PreservesPushout.iso G f g).inv = pushout.inl := by
simp [preserves_pushout.iso, iso.comp_inv_eq]
@@ -365,7 +365,7 @@ lean 3 declaration is
but is expected to have type
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g] [_inst_5 : CategoryTheory.Limits.HasPushout.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C 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(CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W X f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W Y g) _inst_5)
Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inr_iso_inv CategoryTheory.Limits.PreservesPushout.inr_iso_invₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem PreservesPushout.inr_iso_inv :
G.map pushout.inr ≫ (PreservesPushout.iso G f g).inv = pushout.inr := by
simp [preserves_pushout.iso, iso.comp_inv_eq]
mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Andrew Yang
! This file was ported from Lean 3 source module category_theory.limits.preserves.shapes.pullbacks
-! leanprover-community/mathlib commit f11e306adb9f2a393539d2bb4293bf1b42caa7ac
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.Limits.Preserves.Basic
/-!
# Preserving pullbacks
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Constructions to relate the notions of preserving pullbacks and reflecting pullbacks to concrete
pullback cones.
mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5
@@ -127,15 +127,15 @@ def preservesPullbackSymmetry : PreservesLimit (cospan g f) G
#align category_theory.limits.preserves_pullback_symmetry CategoryTheory.Limits.preservesPullbackSymmetry
-/
-/- warning: category_theory.limits.has_pullback_of_preserves_pullback -> CategoryTheory.Limits.hasPullback_of_preserves_pullback is a dubious translation:
+/- warning: category_theory.limits.has_pullback_of_preserves_pullback -> CategoryTheory.Limits.hasPullback_of_preservesPullback is a dubious translation:
lean 3 declaration is
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Z) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y Z) [_inst_3 : CategoryTheory.Limits.PreservesLimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingCospan (CategoryTheory.Limits.WidePullbackShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.cospan.{u1, u3} C _inst_1 X Y Z f g) G] [_inst_4 : CategoryTheory.Limits.HasPullback.{u1, u3} C _inst_1 X Y Z f g], CategoryTheory.Limits.HasPullback.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Z) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X Z f) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y Z g)
but is expected to have type
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Z) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y Z) [_inst_3 : CategoryTheory.Limits.PreservesLimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingCospan (CategoryTheory.Limits.WidePullbackShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.cospan.{u1, u3} C _inst_1 X Y Z f g) G] [_inst_4 : CategoryTheory.Limits.HasPullback.{u1, u3} C _inst_1 X Y Z f g], CategoryTheory.Limits.HasPullback.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Z f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g)
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_pullback_of_preserves_pullback CategoryTheory.Limits.hasPullback_of_preserves_pullbackₓ'. -/
-theorem hasPullback_of_preserves_pullback [HasPullback f g] : HasPullback (G.map f) (G.map g) :=
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_pullback_of_preserves_pullback CategoryTheory.Limits.hasPullback_of_preservesPullbackₓ'. -/
+theorem hasPullback_of_preservesPullback [HasPullback f g] : HasPullback (G.map f) (G.map g) :=
⟨⟨⟨_, isLimitPullbackConeMapOfIsLimit G _ (pullbackIsPullback _ _)⟩⟩⟩
-#align category_theory.limits.has_pullback_of_preserves_pullback CategoryTheory.Limits.hasPullback_of_preserves_pullback
+#align category_theory.limits.has_pullback_of_preserves_pullback CategoryTheory.Limits.hasPullback_of_preservesPullback
variable [HasPullback f g] [HasPullback (G.map f) (G.map g)]
@@ -291,15 +291,15 @@ def preservesPushoutSymmetry : PreservesColimit (span g f) G
#align category_theory.limits.preserves_pushout_symmetry CategoryTheory.Limits.preservesPushoutSymmetry
-/
-/- warning: category_theory.limits.has_pushout_of_preserves_pushout -> CategoryTheory.Limits.hasPushout_of_preserves_pushout is a dubious translation:
+/- warning: category_theory.limits.has_pushout_of_preserves_pushout -> CategoryTheory.Limits.hasPushout_of_preservesPushout is a dubious translation:
lean 3 declaration is
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g], CategoryTheory.Limits.HasPushout.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W X f) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W Y g)
but is expected to have type
forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g], CategoryTheory.Limits.HasPushout.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W X f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W Y g)
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_pushout_of_preserves_pushout CategoryTheory.Limits.hasPushout_of_preserves_pushoutₓ'. -/
-theorem hasPushout_of_preserves_pushout [HasPushout f g] : HasPushout (G.map f) (G.map g) :=
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_pushout_of_preserves_pushout CategoryTheory.Limits.hasPushout_of_preservesPushoutₓ'. -/
+theorem hasPushout_of_preservesPushout [HasPushout f g] : HasPushout (G.map f) (G.map g) :=
⟨⟨⟨_, isColimitPushoutCoconeMapOfIsColimit G _ (pushoutIsPushout _ _)⟩⟩⟩
-#align category_theory.limits.has_pushout_of_preserves_pushout CategoryTheory.Limits.hasPushout_of_preserves_pushout
+#align category_theory.limits.has_pushout_of_preserves_pushout CategoryTheory.Limits.hasPushout_of_preservesPushout
variable [HasPushout f g] [HasPushout (G.map f) (G.map g)]
mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25
@@ -47,6 +47,12 @@ variable (G : C ⥤ D)
variable {W X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z} {h : W ⟶ X} {k : W ⟶ Y} (comm : h ≫ f = k ≫ g)
+/- warning: category_theory.limits.is_limit_map_cone_pullback_cone_equiv -> CategoryTheory.Limits.isLimitMapConePullbackConeEquiv is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_map_cone_pullback_cone_equiv CategoryTheory.Limits.isLimitMapConePullbackConeEquivₓ'. -/
/-- The map of a pullback cone is a limit iff the fork consisting of the mapped morphisms is a
limit. This essentially lets us commute `pullback_cone.mk` with `functor.map_cone`. -/
def isLimitMapConePullbackConeEquiv :
@@ -60,12 +66,24 @@ def isLimitMapConePullbackConeEquiv :
rintro (_ | _ | _) <;> dsimp <;> simp only [comp_id, id_comp, G.map_comp]
#align category_theory.limits.is_limit_map_cone_pullback_cone_equiv CategoryTheory.Limits.isLimitMapConePullbackConeEquiv
+/- warning: category_theory.limits.is_limit_pullback_cone_map_of_is_limit -> CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimit is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_pullback_cone_map_of_is_limit CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimitₓ'. -/
/-- The property of preserving pullbacks expressed in terms of binary fans. -/
def isLimitPullbackConeMapOfIsLimit [PreservesLimit (cospan f g) G]
(l : IsLimit (PullbackCone.mk h k comm)) : IsLimit (PullbackCone.mk (G.map h) (G.map k) _) :=
isLimitMapConePullbackConeEquiv G comm (PreservesLimit.preserves l)
#align category_theory.limits.is_limit_pullback_cone_map_of_is_limit CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimit
+/- warning: category_theory.limits.is_limit_of_is_limit_pullback_cone_map -> CategoryTheory.Limits.isLimitOfIsLimitPullbackConeMap is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_of_is_limit_pullback_cone_map CategoryTheory.Limits.isLimitOfIsLimitPullbackConeMapₓ'. -/
/-- The property of reflecting pullbacks expressed in terms of binary fans. -/
def isLimitOfIsLimitPullbackConeMap [ReflectsLimit (cospan f g) G]
(l : IsLimit (PullbackCone.mk (G.map h) (G.map k) _)) : IsLimit (PullbackCone.mk h k comm) :=
@@ -74,6 +92,12 @@ def isLimitOfIsLimitPullbackConeMap [ReflectsLimit (cospan f g) G]
variable (f g) [PreservesLimit (cospan f g) G]
+/- warning: category_theory.limits.is_limit_of_has_pullback_of_preserves_limit -> CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimit is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit_of_has_pullback_of_preserves_limit CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimitₓ'. -/
/-- If `G` preserves pullbacks and `C` has them, then the pullback cone constructed of the mapped
morphisms of the pullback cone is a limit. -/
def isLimitOfHasPullbackOfPreservesLimit [HasPullback f g] :
@@ -81,6 +105,7 @@ def isLimitOfHasPullbackOfPreservesLimit [HasPullback f g] :
isLimitPullbackConeMapOfIsLimit G _ (pullbackIsPullback f g)
#align category_theory.limits.is_limit_of_has_pullback_of_preserves_limit CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimit
+#print CategoryTheory.Limits.preservesPullbackSymmetry /-
/-- If `F` preserves the pullback of `f, g`, it also preserves the pullback of `g, f`. -/
def preservesPullbackSymmetry : PreservesLimit (cospan g f) G
where preserves c hc :=
@@ -100,37 +125,74 @@ def preservesPullbackSymmetry : PreservesLimit (cospan g f) G
(c.π.naturality walking_cospan.hom.inr).symm.trans
(c.π.naturality walking_cospan.hom.inl : _)
#align category_theory.limits.preserves_pullback_symmetry CategoryTheory.Limits.preservesPullbackSymmetry
+-/
+/- warning: category_theory.limits.has_pullback_of_preserves_pullback -> CategoryTheory.Limits.hasPullback_of_preserves_pullback is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_pullback_of_preserves_pullback CategoryTheory.Limits.hasPullback_of_preserves_pullbackₓ'. -/
theorem hasPullback_of_preserves_pullback [HasPullback f g] : HasPullback (G.map f) (G.map g) :=
⟨⟨⟨_, isLimitPullbackConeMapOfIsLimit G _ (pullbackIsPullback _ _)⟩⟩⟩
#align category_theory.limits.has_pullback_of_preserves_pullback CategoryTheory.Limits.hasPullback_of_preserves_pullback
variable [HasPullback f g] [HasPullback (G.map f) (G.map g)]
+/- warning: category_theory.limits.preserves_pullback.iso -> CategoryTheory.Limits.PreservesPullback.iso is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso CategoryTheory.Limits.PreservesPullback.isoₓ'. -/
/-- If `G` preserves the pullback of `(f,g)`, then the pullback comparison map for `G` at `(f,g)` is
an isomorphism. -/
def PreservesPullback.iso : G.obj (pullback f g) ≅ pullback (G.map f) (G.map g) :=
IsLimit.conePointUniqueUpToIso (isLimitOfHasPullbackOfPreservesLimit G f g) (limit.isLimit _)
#align category_theory.limits.preserves_pullback.iso CategoryTheory.Limits.PreservesPullback.iso
+/- warning: category_theory.limits.preserves_pullback.iso_hom_fst -> CategoryTheory.Limits.PreservesPullback.iso_hom_fst is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_hom_fst CategoryTheory.Limits.PreservesPullback.iso_hom_fstₓ'. -/
@[reassoc.1]
theorem PreservesPullback.iso_hom_fst :
(PreservesPullback.iso G f g).Hom ≫ pullback.fst = G.map pullback.fst := by
simp [preserves_pullback.iso]
#align category_theory.limits.preserves_pullback.iso_hom_fst CategoryTheory.Limits.PreservesPullback.iso_hom_fst
+/- warning: category_theory.limits.preserves_pullback.iso_hom_snd -> CategoryTheory.Limits.PreservesPullback.iso_hom_snd is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_hom_snd CategoryTheory.Limits.PreservesPullback.iso_hom_sndₓ'. -/
@[reassoc.1]
theorem PreservesPullback.iso_hom_snd :
(PreservesPullback.iso G f g).Hom ≫ pullback.snd = G.map pullback.snd := by
simp [preserves_pullback.iso]
#align category_theory.limits.preserves_pullback.iso_hom_snd CategoryTheory.Limits.PreservesPullback.iso_hom_snd
+/- warning: category_theory.limits.preserves_pullback.iso_inv_fst -> CategoryTheory.Limits.PreservesPullback.iso_inv_fst is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_inv_fst CategoryTheory.Limits.PreservesPullback.iso_inv_fstₓ'. -/
@[simp, reassoc.1]
theorem PreservesPullback.iso_inv_fst :
(PreservesPullback.iso G f g).inv ≫ G.map pullback.fst = pullback.fst := by
simp [preserves_pullback.iso, iso.inv_comp_eq]
#align category_theory.limits.preserves_pullback.iso_inv_fst CategoryTheory.Limits.PreservesPullback.iso_inv_fst
+/- warning: category_theory.limits.preserves_pullback.iso_inv_snd -> CategoryTheory.Limits.PreservesPullback.iso_inv_snd is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Z) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y Z) [_inst_3 : CategoryTheory.Limits.PreservesLimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingCospan (CategoryTheory.Limits.WidePullbackShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.cospan.{u1, u3} C _inst_1 X Y Z f g) G] [_inst_4 : CategoryTheory.Limits.HasPullback.{u1, u3} C _inst_1 X Y Z f g] [_inst_5 : CategoryTheory.Limits.HasPullback.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C 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_inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y Z g) _inst_5) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pullback.{u1, u3} C _inst_1 X Y Z f g _inst_4)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (CategoryTheory.Iso.inv.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C 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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_inv_snd CategoryTheory.Limits.PreservesPullback.iso_inv_sndₓ'. -/
@[simp, reassoc.1]
theorem PreservesPullback.iso_inv_snd :
(PreservesPullback.iso G f g).inv ≫ G.map pullback.snd = pullback.snd := by
@@ -149,6 +211,12 @@ variable (G : C ⥤ D)
variable {W X Y Z : C} {h : X ⟶ Z} {k : Y ⟶ Z} {f : W ⟶ X} {g : W ⟶ Y} (comm : f ≫ h = g ≫ k)
+/- warning: category_theory.limits.is_colimit_map_cocone_pushout_cocone_equiv -> CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquiv is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_map_cocone_pushout_cocone_equiv CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquivₓ'. -/
/-- The map of a pushout cocone is a colimit iff the cofork consisting of the mapped morphisms is a
colimit. This essentially lets us commute `pushout_cocone.mk` with `functor.map_cocone`. -/
def isColimitMapCoconePushoutCoconeEquiv :
@@ -163,6 +231,12 @@ def isColimitMapCoconePushoutCoconeEquiv :
simp only [category.comp_id, category.id_comp, ← G.map_comp]
#align category_theory.limits.is_colimit_map_cocone_pushout_cocone_equiv CategoryTheory.Limits.isColimitMapCoconePushoutCoconeEquiv
+/- warning: category_theory.limits.is_colimit_pushout_cocone_map_of_is_colimit -> CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimit is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_pushout_cocone_map_of_is_colimit CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimitₓ'. -/
/-- The property of preserving pushouts expressed in terms of binary cofans. -/
def isColimitPushoutCoconeMapOfIsColimit [PreservesColimit (span f g) G]
(l : IsColimit (PushoutCocone.mk h k comm)) :
@@ -170,6 +244,12 @@ def isColimitPushoutCoconeMapOfIsColimit [PreservesColimit (span f g) G]
isColimitMapCoconePushoutCoconeEquiv G comm (PreservesColimit.preserves l)
#align category_theory.limits.is_colimit_pushout_cocone_map_of_is_colimit CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimit
+/- warning: category_theory.limits.is_colimit_of_is_colimit_pushout_cocone_map -> CategoryTheory.Limits.isColimitOfIsColimitPushoutCoconeMap is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} {Z : C} {h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Z} {k : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y Z} {f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X} {g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y} (comm : Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Z) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) W X Z f h) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) W Y Z g k)) [_inst_3 : CategoryTheory.Limits.ReflectsColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G], (CategoryTheory.Limits.IsColimit.{0, u2, 0, u4} CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) D _inst_2 (CategoryTheory.Limits.span.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D 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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_of_is_colimit_pushout_cocone_map CategoryTheory.Limits.isColimitOfIsColimitPushoutCoconeMapₓ'. -/
/-- The property of reflecting pushouts expressed in terms of binary cofans. -/
def isColimitOfIsColimitPushoutCoconeMap [ReflectsColimit (span f g) G]
(l : IsColimit (PushoutCocone.mk (G.map h) (G.map k) _)) :
@@ -179,6 +259,12 @@ def isColimitOfIsColimitPushoutCoconeMap [ReflectsColimit (span f g) G]
variable (f g) [PreservesColimit (span f g) G]
+/- warning: category_theory.limits.is_colimit_of_has_pushout_of_preserves_colimit -> CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimit is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g], CategoryTheory.Limits.IsColimit.{0, u2, 0, u4} CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) D _inst_2 (CategoryTheory.Limits.span.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W X f) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W Y g)) (CategoryTheory.Limits.PushoutCocone.mk.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W X f) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W Y g) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G (CategoryTheory.Limits.pushout.{u1, u3} C _inst_1 W X Y f g _inst_4)) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X (CategoryTheory.Limits.pushout.{u1, u3} C _inst_1 W X Y f g _inst_4) (CategoryTheory.Limits.pushout.inl.{u1, u3} C _inst_1 W X Y f g _inst_4)) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y (CategoryTheory.Limits.pushout.{u1, u3} C _inst_1 W X Y f g _inst_4) (CategoryTheory.Limits.pushout.inr.{u1, u3} C _inst_1 W X Y f g _inst_4)) (CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimit._proof_1.{u3, u4, u1, u2} C _inst_1 D _inst_2 G W X Y f g _inst_4))
+but is expected to have type
+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g], CategoryTheory.Limits.IsColimit.{0, u2, 0, u4} CategoryTheory.Limits.WalkingSpan 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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit_of_has_pushout_of_preserves_colimit CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimitₓ'. -/
/-- If `G` preserves pushouts and `C` has them, then the pushout cocone constructed of the mapped
morphisms of the pushout cocone is a colimit. -/
def isColimitOfHasPushoutOfPreservesColimit [HasPushout f g] :
@@ -186,6 +272,7 @@ def isColimitOfHasPushoutOfPreservesColimit [HasPushout f g] :
isColimitPushoutCoconeMapOfIsColimit G _ (pushoutIsPushout f g)
#align category_theory.limits.is_colimit_of_has_pushout_of_preserves_colimit CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimit
+#print CategoryTheory.Limits.preservesPushoutSymmetry /-
/-- If `F` preserves the pushout of `f, g`, it also preserves the pushout of `g, f`. -/
def preservesPushoutSymmetry : PreservesColimit (span g f) G
where preserves c hc :=
@@ -202,13 +289,26 @@ def preservesPushoutSymmetry : PreservesColimit (span g f) G
exact (is_colimit.precompose_hom_equiv (diagramIsoSpan.{v₁} _) _).invFun hc
· exact (c.ι.naturality walking_span.hom.snd).trans (c.ι.naturality walking_span.hom.fst).symm
#align category_theory.limits.preserves_pushout_symmetry CategoryTheory.Limits.preservesPushoutSymmetry
+-/
+/- warning: category_theory.limits.has_pushout_of_preserves_pushout -> CategoryTheory.Limits.hasPushout_of_preserves_pushout is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g], CategoryTheory.Limits.HasPushout.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W X f) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W Y g)
+but is expected to have type
+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g], CategoryTheory.Limits.HasPushout.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W X f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W Y g)
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_pushout_of_preserves_pushout CategoryTheory.Limits.hasPushout_of_preserves_pushoutₓ'. -/
theorem hasPushout_of_preserves_pushout [HasPushout f g] : HasPushout (G.map f) (G.map g) :=
⟨⟨⟨_, isColimitPushoutCoconeMapOfIsColimit G _ (pushoutIsPushout _ _)⟩⟩⟩
#align category_theory.limits.has_pushout_of_preserves_pushout CategoryTheory.Limits.hasPushout_of_preserves_pushout
variable [HasPushout f g] [HasPushout (G.map f) (G.map g)]
+/- warning: category_theory.limits.preserves_pushout.iso -> CategoryTheory.Limits.PreservesPushout.iso is a dubious translation:
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+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g] [_inst_5 : CategoryTheory.Limits.HasPushout.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W X f) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W Y g)], CategoryTheory.Iso.{u2, u4} D _inst_2 (CategoryTheory.Limits.pushout.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W X f) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G W Y g) _inst_5) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G (CategoryTheory.Limits.pushout.{u1, u3} C _inst_1 W X Y f g _inst_4))
+but is expected to have type
+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {W : C} {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W X) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) W Y) [_inst_3 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u2, u3, u4} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u3} C _inst_1 W X Y f g) G] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} C _inst_1 W X Y f g] [_inst_5 : CategoryTheory.Limits.HasPushout.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C 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_inst_1 D _inst_2 G) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W X f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) W Y g)], CategoryTheory.Iso.{u2, u4} D _inst_2 (CategoryTheory.Limits.pushout.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D 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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.iso CategoryTheory.Limits.PreservesPushout.isoₓ'. -/
/-- If `G` preserves the pushout of `(f,g)`, then the pushout comparison map for `G` at `(f,g)` is
an isomorphism. -/
def PreservesPushout.iso : pushout (G.map f) (G.map g) ≅ G.obj (pushout f g) :=
@@ -216,6 +316,12 @@ def PreservesPushout.iso : pushout (G.map f) (G.map g) ≅ G.obj (pushout f g) :
(isColimitOfHasPushoutOfPreservesColimit G f g)
#align category_theory.limits.preserves_pushout.iso CategoryTheory.Limits.PreservesPushout.iso
+/- warning: category_theory.limits.preserves_pushout.inl_iso_hom -> CategoryTheory.Limits.PreservesPushout.inl_iso_hom is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inl_iso_hom CategoryTheory.Limits.PreservesPushout.inl_iso_homₓ'. -/
@[reassoc.1]
theorem PreservesPushout.inl_iso_hom :
pushout.inl ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inl :=
@@ -224,6 +330,12 @@ theorem PreservesPushout.inl_iso_hom :
simp
#align category_theory.limits.preserves_pushout.inl_iso_hom CategoryTheory.Limits.PreservesPushout.inl_iso_hom
+/- warning: category_theory.limits.preserves_pushout.inr_iso_hom -> CategoryTheory.Limits.PreservesPushout.inr_iso_hom is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inr_iso_hom CategoryTheory.Limits.PreservesPushout.inr_iso_homₓ'. -/
@[reassoc.1]
theorem PreservesPushout.inr_iso_hom :
pushout.inr ≫ (PreservesPushout.iso G f g).Hom = G.map pushout.inr :=
@@ -232,12 +344,24 @@ theorem PreservesPushout.inr_iso_hom :
simp
#align category_theory.limits.preserves_pushout.inr_iso_hom CategoryTheory.Limits.PreservesPushout.inr_iso_hom
+/- warning: category_theory.limits.preserves_pushout.inl_iso_inv -> CategoryTheory.Limits.PreservesPushout.inl_iso_inv is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inl_iso_inv CategoryTheory.Limits.PreservesPushout.inl_iso_invₓ'. -/
@[simp, reassoc.1]
theorem PreservesPushout.inl_iso_inv :
G.map pushout.inl ≫ (PreservesPushout.iso G f g).inv = pushout.inl := by
simp [preserves_pushout.iso, iso.comp_inv_eq]
#align category_theory.limits.preserves_pushout.inl_iso_inv CategoryTheory.Limits.PreservesPushout.inl_iso_inv
+/- warning: category_theory.limits.preserves_pushout.inr_iso_inv -> CategoryTheory.Limits.PreservesPushout.inr_iso_inv is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.inr_iso_inv CategoryTheory.Limits.PreservesPushout.inr_iso_invₓ'. -/
@[simp, reassoc.1]
theorem PreservesPushout.inr_iso_inv :
G.map pushout.inr ≫ (PreservesPushout.iso G f g).inv = pushout.inr := by
@@ -260,6 +384,12 @@ variable {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z}
variable [HasPullback f g] [HasPullback (G.map f) (G.map g)]
+/- warning: category_theory.limits.preserves_pullback.of_iso_comparison -> CategoryTheory.Limits.PreservesPullback.ofIsoComparison is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} D] (G : CategoryTheory.Functor.{u1, u1, u2, u3} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} {f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Z} {g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z} [_inst_3 : CategoryTheory.Limits.HasPullback.{u1, u2} C _inst_1 X Y Z f g] [_inst_4 : CategoryTheory.Limits.HasPullback.{u1, u3} D _inst_2 (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Z) (CategoryTheory.Functor.map.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X Z f) (CategoryTheory.Functor.map.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Y Z g)] [i : CategoryTheory.IsIso.{u1, u3} D _inst_2 (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G (CategoryTheory.Limits.pullback.{u1, u2} C _inst_1 X Y Z f g _inst_3)) (CategoryTheory.Limits.pullback.{u1, u3} D _inst_2 (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Z) (CategoryTheory.Functor.map.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X Z f) (CategoryTheory.Functor.map.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Y Z g) _inst_4) (CategoryTheory.Limits.pullbackComparison.{u1, u1, u2, u3} C _inst_1 D _inst_2 X Y Z G f g _inst_3 _inst_4)], CategoryTheory.Limits.PreservesLimit.{0, 0, u1, u1, u2, u3} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingCospan (CategoryTheory.Limits.WidePullbackShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.cospan.{u1, u2} C _inst_1 X Y Z f g) G
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.of_iso_comparison CategoryTheory.Limits.PreservesPullback.ofIsoComparisonₓ'. -/
/-- If the pullback comparison map for `G` at `(f,g)` is an isomorphism, then `G` preserves the
pullback of `(f,g)`. -/
def PreservesPullback.ofIsoComparison [i : IsIso (pullbackComparison G f g)] :
@@ -273,6 +403,12 @@ def PreservesPullback.ofIsoComparison [i : IsIso (pullbackComparison G f g)] :
variable [PreservesLimit (cospan f g) G]
+/- warning: category_theory.limits.preserves_pullback.iso_hom -> CategoryTheory.Limits.PreservesPullback.iso_hom is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pullback.iso_hom CategoryTheory.Limits.PreservesPullback.iso_homₓ'. -/
@[simp]
theorem PreservesPullback.iso_hom : (PreservesPullback.iso G f g).Hom = pullbackComparison G f g :=
rfl
@@ -291,6 +427,12 @@ variable {X Y Z : C} {f : X ⟶ Y} {g : X ⟶ Z}
variable [HasPushout f g] [HasPushout (G.map f) (G.map g)]
+/- warning: category_theory.limits.preserves_pushout.of_iso_comparison -> CategoryTheory.Limits.PreservesPushout.ofIsoComparison is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u2} C _inst_1 X Y Z f g) G
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.of_iso_comparison CategoryTheory.Limits.PreservesPushout.ofIsoComparisonₓ'. -/
/-- If the pushout comparison map for `G` at `(f,g)` is an isomorphism, then `G` preserves the
pushout of `(f,g)`. -/
def PreservesPushout.ofIsoComparison [i : IsIso (pushoutComparison G f g)] :
@@ -304,6 +446,12 @@ def PreservesPushout.ofIsoComparison [i : IsIso (pushoutComparison G f g)] :
variable [PreservesColimit (span f g) G]
+/- warning: category_theory.limits.preserves_pushout.iso_hom -> CategoryTheory.Limits.PreservesPushout.iso_hom is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} D] (G : CategoryTheory.Functor.{u1, u1, u2, u3} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} {f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y} {g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Z} [_inst_3 : CategoryTheory.Limits.HasPushout.{u1, u2} C _inst_1 X Y Z f g] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} D _inst_2 (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Z) (CategoryTheory.Functor.map.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X Y f) (CategoryTheory.Functor.map.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X Z g)] [_inst_5 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u1, u2, u3} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u2} C _inst_1 X Y Z f g) G], Eq.{succ u1} (Quiver.Hom.{succ u1, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Limits.pushout.{u1, u3} D _inst_2 (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Z) (CategoryTheory.Functor.map.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X Y f) (CategoryTheory.Functor.map.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X Z g) _inst_4) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G (CategoryTheory.Limits.pushout.{u1, u2} C _inst_1 X Y Z f g _inst_3))) (CategoryTheory.Iso.hom.{u1, u3} D _inst_2 (CategoryTheory.Limits.pushout.{u1, u3} D _inst_2 (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G Z) (CategoryTheory.Functor.map.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X Y f) (CategoryTheory.Functor.map.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X Z g) _inst_4) (CategoryTheory.Functor.obj.{u1, u1, u2, u3} C _inst_1 D _inst_2 G (CategoryTheory.Limits.pushout.{u1, u2} C _inst_1 X Y Z f g _inst_3)) (CategoryTheory.Limits.PreservesPushout.iso.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X Y Z f g _inst_5 _inst_3 _inst_4)) (CategoryTheory.Limits.pushoutComparison.{u1, u1, u2, u3} C _inst_1 D _inst_2 X Y Z G f g _inst_3 _inst_4)
+but is expected to have type
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} D] (G : CategoryTheory.Functor.{u1, u1, u2, u3} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} {f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y} {g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Z} [_inst_3 : CategoryTheory.Limits.HasPushout.{u1, u2} C _inst_1 X Y Z f g] [_inst_4 : CategoryTheory.Limits.HasPushout.{u1, u3} D _inst_2 (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Y f) (Prefunctor.map.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Z g)] [_inst_5 : CategoryTheory.Limits.PreservesColimit.{0, 0, u1, u1, u2, u3} C _inst_1 D _inst_2 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{u1, u2} C _inst_1 X Y Z f g) G], Eq.{succ u1} (Quiver.Hom.{succ u1, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Limits.pushout.{u1, u3} D _inst_2 (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Y f) (Prefunctor.map.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Z g) _inst_4) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pushout.{u1, u2} C _inst_1 X Y Z f g _inst_3))) (CategoryTheory.Iso.hom.{u1, u3} D _inst_2 (CategoryTheory.Limits.pushout.{u1, u3} D _inst_2 (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) Y) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) Z) (Prefunctor.map.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Y f) (Prefunctor.map.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) X Z g) _inst_4) (Prefunctor.obj.{succ u1, succ u1, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} D (CategoryTheory.Category.toCategoryStruct.{u1, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u3} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.pushout.{u1, u2} C _inst_1 X Y Z f g _inst_3)) (CategoryTheory.Limits.PreservesPushout.iso.{u1, u1, u2, u3} C _inst_1 D _inst_2 G X Y Z f g _inst_5 _inst_3 _inst_4)) (CategoryTheory.Limits.pushoutComparison.{u1, u1, u2, u3} C _inst_1 D _inst_2 X Y Z G f g _inst_3 _inst_4)
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.preserves_pushout.iso_hom CategoryTheory.Limits.PreservesPushout.iso_homₓ'. -/
@[simp]
theorem PreservesPushout.iso_hom : (PreservesPushout.iso G f g).Hom = pushoutComparison G f g :=
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
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)
@@ -38,11 +38,8 @@ namespace CategoryTheory.Limits
section Pullback
variable {C : Type u₁} [Category.{v₁} C]
-
variable {D : Type u₂} [Category.{v₂} D]
-
variable (G : C ⥤ D)
-
variable {W X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z} {h : W ⟶ X} {k : W ⟶ Y} (comm : h ≫ f = k ≫ g)
/-- The map of a pullback cone is a limit iff the fork consisting of the mapped morphisms is a
@@ -143,11 +140,8 @@ end Pullback
section Pushout
variable {C : Type u₁} [Category.{v₁} C]
-
variable {D : Type u₂} [Category.{v₂} D]
-
variable (G : C ⥤ D)
-
variable {W X Y Z : C} {h : X ⟶ Z} {k : Y ⟶ Z} {f : W ⟶ X} {g : W ⟶ Y} (comm : f ≫ h = g ≫ k)
/-- The map of a pushout cocone is a colimit iff the cofork consisting of the mapped morphisms is a
@@ -248,15 +242,12 @@ end Pushout
section
variable {C : Type u₁} [Category.{v₁} C]
-
variable {D : Type u₂} [Category.{v₁} D]
-
variable (G : C ⥤ D)
section Pullback
variable {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z}
-
variable [HasPullback f g] [HasPullback (G.map f) (G.map g)]
/-- If the pullback comparison map for `G` at `(f,g)` is an isomorphism, then `G` preserves the
@@ -285,7 +276,6 @@ end Pullback
section Pushout
variable {X Y Z : C} {f : X ⟶ Y} {g : X ⟶ Z}
-
variable [HasPushout f g] [HasPushout (G.map f) (G.map g)]
/-- If the pushout comparison map for `G` at `(f,g)` is an isomorphism, then `G` preserves the
In this PR, it is shown that monomorphisms can be characterized in terms of pullback squares. Future applications of this include the fact that if a family of functors reflects isomorphisms, it shall also reflect monomorphisms and epimorphisms (provided suitable limits/colimits exist).
@@ -89,12 +89,12 @@ def preservesPullbackSymmetry : PreservesLimit (cospan g f) G where
preserves {c} hc := by
apply (IsLimit.postcomposeHomEquiv (diagramIsoCospan.{v₂} _) _).toFun
apply IsLimit.ofIsoLimit _ (PullbackCone.isoMk _).symm
- apply PullbackCone.flipIsLimit
+ apply PullbackCone.isLimitOfFlip
apply (isLimitMapConePullbackConeEquiv _ _).toFun
· refine @PreservesLimit.preserves _ _ _ _ _ _ _ _ ?_ _ ?_
· dsimp
infer_instance
- apply PullbackCone.flipIsLimit
+ apply PullbackCone.isLimitOfFlip
apply IsLimit.ofIsoLimit _ (PullbackCone.isoMk _)
exact (IsLimit.postcomposeHomEquiv (diagramIsoCospan.{v₁} _) _).invFun hc
· exact
@@ -196,15 +196,12 @@ def preservesPushoutSymmetry : PreservesColimit (span g f) G where
preserves {c} hc := by
apply (IsColimit.precomposeHomEquiv (diagramIsoSpan.{v₂} _).symm _).toFun
apply IsColimit.ofIsoColimit _ (PushoutCocone.isoMk _).symm
- apply PushoutCocone.flipIsColimit
+ apply PushoutCocone.isColimitOfFlip
apply (isColimitMapCoconePushoutCoconeEquiv _ _).toFun
· refine @PreservesColimit.preserves _ _ _ _ _ _ _ _ ?_ _ ?_ -- Porting note: more TC coddling
· dsimp
infer_instance
- apply PushoutCocone.flipIsColimit
- apply IsColimit.ofIsoColimit _ (PushoutCocone.isoMk _)
- exact (IsColimit.precomposeHomEquiv (diagramIsoSpan.{v₁} _) _).invFun hc
- · exact (c.ι.naturality WalkingSpan.Hom.snd).trans (c.ι.naturality WalkingSpan.Hom.fst).symm
+ · exact PushoutCocone.flipIsColimit hc
#align category_theory.limits.preserves_pushout_symmetry CategoryTheory.Limits.preservesPushoutSymmetry
theorem hasPushout_of_preservesPushout [HasPushout f g] : HasPushout (G.map f) (G.map g) :=
@@ -61,7 +61,7 @@ def isLimitMapConePullbackConeEquiv :
/-- The property of preserving pullbacks expressed in terms of binary fans. -/
def isLimitPullbackConeMapOfIsLimit [PreservesLimit (cospan f g) G]
(l : IsLimit (PullbackCone.mk h k comm)) :
- have : G.map h ≫ G.map f = G.map k ≫ G.map g := by rw [←G.map_comp,←G.map_comp,comm]
+ have : G.map h ≫ G.map f = G.map k ≫ G.map g := by rw [← G.map_comp, ← G.map_comp,comm]
IsLimit (PullbackCone.mk (G.map h) (G.map k) this) :=
isLimitMapConePullbackConeEquiv G comm (PreservesLimit.preserves l)
#align category_theory.limits.is_limit_pullback_cone_map_of_is_limit CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimit
@@ -69,7 +69,7 @@ def isLimitPullbackConeMapOfIsLimit [PreservesLimit (cospan f g) G]
/-- The property of reflecting pullbacks expressed in terms of binary fans. -/
def isLimitOfIsLimitPullbackConeMap [ReflectsLimit (cospan f g) G]
(l : IsLimit (PullbackCone.mk (G.map h) (G.map k) (show G.map h ≫ G.map f = G.map k ≫ G.map g
- from by simp only [←G.map_comp,comm]))) : IsLimit (PullbackCone.mk h k comm) :=
+ from by simp only [← G.map_comp,comm]))) : IsLimit (PullbackCone.mk h k comm) :=
ReflectsLimit.reflects ((isLimitMapConePullbackConeEquiv G comm).symm l)
#align category_theory.limits.is_limit_of_is_limit_pullback_cone_map CategoryTheory.Limits.isLimitOfIsLimitPullbackConeMap
@@ -79,7 +79,7 @@ variable (f g) [PreservesLimit (cospan f g) G]
morphisms of the pullback cone is a limit. -/
def isLimitOfHasPullbackOfPreservesLimit [i : HasPullback f g] :
have : G.map pullback.fst ≫ G.map f = G.map pullback.snd ≫ G.map g := by
- simp only [←G.map_comp, pullback.condition];
+ simp only [← G.map_comp, pullback.condition];
IsLimit (PullbackCone.mk (G.map (@pullback.fst _ _ _ _ _ f g i)) (G.map pullback.snd) this) :=
isLimitPullbackConeMapOfIsLimit G _ (pullbackIsPullback f g)
#align category_theory.limits.is_limit_of_has_pullback_of_preserves_limit CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimit
@@ -168,14 +168,14 @@ def isColimitMapCoconePushoutCoconeEquiv :
def isColimitPushoutCoconeMapOfIsColimit [PreservesColimit (span f g) G]
(l : IsColimit (PushoutCocone.mk h k comm)) :
IsColimit (PushoutCocone.mk (G.map h) (G.map k) (show G.map f ≫ G.map h = G.map g ≫ G.map k
- from by simp only [←G.map_comp,comm] )) :=
+ from by simp only [← G.map_comp,comm] )) :=
isColimitMapCoconePushoutCoconeEquiv G comm (PreservesColimit.preserves l)
#align category_theory.limits.is_colimit_pushout_cocone_map_of_is_colimit CategoryTheory.Limits.isColimitPushoutCoconeMapOfIsColimit
/-- The property of reflecting pushouts expressed in terms of binary cofans. -/
def isColimitOfIsColimitPushoutCoconeMap [ReflectsColimit (span f g) G]
(l : IsColimit (PushoutCocone.mk (G.map h) (G.map k) (show G.map f ≫ G.map h =
- G.map g ≫ G.map k from by simp only [←G.map_comp,comm]))) :
+ G.map g ≫ G.map k from by simp only [← G.map_comp,comm]))) :
IsColimit (PushoutCocone.mk h k comm) :=
ReflectsColimit.reflects ((isColimitMapCoconePushoutCoconeEquiv G comm).symm l)
#align category_theory.limits.is_colimit_of_is_colimit_pushout_cocone_map CategoryTheory.Limits.isColimitOfIsColimitPushoutCoconeMap
@@ -2,15 +2,12 @@
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Andrew Yang
-
-! This file was ported from Lean 3 source module category_theory.limits.preserves.shapes.pullbacks
-! leanprover-community/mathlib commit f11e306adb9f2a393539d2bb4293bf1b42caa7ac
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullbacks
import Mathlib.CategoryTheory.Limits.Preserves.Basic
+#align_import category_theory.limits.preserves.shapes.pullbacks from "leanprover-community/mathlib"@"f11e306adb9f2a393539d2bb4293bf1b42caa7ac"
+
/-!
# Preserving pullbacks
@@ -81,7 +81,7 @@ variable (f g) [PreservesLimit (cospan f g) G]
/-- If `G` preserves pullbacks and `C` has them, then the pullback cone constructed of the mapped
morphisms of the pullback cone is a limit. -/
def isLimitOfHasPullbackOfPreservesLimit [i : HasPullback f g] :
- have : G.map pullback.fst ≫ G.map f = G.map pullback.snd ≫ G.map g := by
+ have : G.map pullback.fst ≫ G.map f = G.map pullback.snd ≫ G.map g := by
simp only [←G.map_comp, pullback.condition];
IsLimit (PullbackCone.mk (G.map (@pullback.fst _ _ _ _ _ f g i)) (G.map pullback.snd) this) :=
isLimitPullbackConeMapOfIsLimit G _ (pullbackIsPullback f g)
by
s! (#3825)
This PR puts, with one exception, every single remaining by
that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh
. The exception is when the by
begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.
Essentially this is s/\n *by$/ by/g
, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated by
s".
@@ -196,8 +196,7 @@ def isColimitOfHasPushoutOfPreservesColimit [i : HasPushout f g] :
/-- If `F` preserves the pushout of `f, g`, it also preserves the pushout of `g, f`. -/
def preservesPushoutSymmetry : PreservesColimit (span g f) G where
- preserves {c} hc :=
- by
+ preserves {c} hc := by
apply (IsColimit.precomposeHomEquiv (diagramIsoSpan.{v₂} _).symm _).toFun
apply IsColimit.ofIsoColimit _ (PushoutCocone.isoMk _).symm
apply PushoutCocone.flipIsColimit
@@ -105,9 +105,9 @@ def preservesPullbackSymmetry : PreservesLimit (cospan g f) G where
(c.π.naturality WalkingCospan.Hom.inl : _)
#align category_theory.limits.preserves_pullback_symmetry CategoryTheory.Limits.preservesPullbackSymmetry
-theorem hasPullback_of_preserves_pullback [HasPullback f g] : HasPullback (G.map f) (G.map g) :=
+theorem hasPullback_of_preservesPullback [HasPullback f g] : HasPullback (G.map f) (G.map g) :=
⟨⟨⟨_, isLimitPullbackConeMapOfIsLimit G _ (pullbackIsPullback _ _)⟩⟩⟩
-#align category_theory.limits.has_pullback_of_preserves_pullback CategoryTheory.Limits.hasPullback_of_preserves_pullback
+#align category_theory.limits.has_pullback_of_preserves_pullback CategoryTheory.Limits.hasPullback_of_preservesPullback
variable [HasPullback f g] [HasPullback (G.map f) (G.map g)]
@@ -211,9 +211,9 @@ def preservesPushoutSymmetry : PreservesColimit (span g f) G where
· exact (c.ι.naturality WalkingSpan.Hom.snd).trans (c.ι.naturality WalkingSpan.Hom.fst).symm
#align category_theory.limits.preserves_pushout_symmetry CategoryTheory.Limits.preservesPushoutSymmetry
-theorem hasPushout_of_preserves_pushout [HasPushout f g] : HasPushout (G.map f) (G.map g) :=
+theorem hasPushout_of_preservesPushout [HasPushout f g] : HasPushout (G.map f) (G.map g) :=
⟨⟨⟨_, isColimitPushoutCoconeMapOfIsColimit G _ (pushoutIsPushout _ _)⟩⟩⟩
-#align category_theory.limits.has_pushout_of_preserves_pushout CategoryTheory.Limits.hasPushout_of_preserves_pushout
+#align category_theory.limits.has_pushout_of_preserves_pushout CategoryTheory.Limits.hasPushout_of_preservesPushout
variable [HasPushout f g] [HasPushout (G.map f) (G.map g)]
@@ -63,8 +63,8 @@ def isLimitMapConePullbackConeEquiv :
/-- The property of preserving pullbacks expressed in terms of binary fans. -/
def isLimitPullbackConeMapOfIsLimit [PreservesLimit (cospan f g) G]
- (l : IsLimit (PullbackCone.mk h k comm)) :
- have : G.map h ≫ G.map f = G.map k ≫ G.map g := by rw [←G.map_comp,←G.map_comp,comm]
+ (l : IsLimit (PullbackCone.mk h k comm)) :
+ have : G.map h ≫ G.map f = G.map k ≫ G.map g := by rw [←G.map_comp,←G.map_comp,comm]
IsLimit (PullbackCone.mk (G.map h) (G.map k) this) :=
isLimitMapConePullbackConeEquiv G comm (PreservesLimit.preserves l)
#align category_theory.limits.is_limit_pullback_cone_map_of_is_limit CategoryTheory.Limits.isLimitPullbackConeMapOfIsLimit
@@ -81,14 +81,14 @@ variable (f g) [PreservesLimit (cospan f g) G]
/-- If `G` preserves pullbacks and `C` has them, then the pullback cone constructed of the mapped
morphisms of the pullback cone is a limit. -/
def isLimitOfHasPullbackOfPreservesLimit [i : HasPullback f g] :
- have : G.map pullback.fst ≫ G.map f = G.map pullback.snd ≫ G.map g := by
+ have : G.map pullback.fst ≫ G.map f = G.map pullback.snd ≫ G.map g := by
simp only [←G.map_comp, pullback.condition];
IsLimit (PullbackCone.mk (G.map (@pullback.fst _ _ _ _ _ f g i)) (G.map pullback.snd) this) :=
isLimitPullbackConeMapOfIsLimit G _ (pullbackIsPullback f g)
#align category_theory.limits.is_limit_of_has_pullback_of_preserves_limit CategoryTheory.Limits.isLimitOfHasPullbackOfPreservesLimit
/-- If `F` preserves the pullback of `f, g`, it also preserves the pullback of `g, f`. -/
-def preservesPullbackSymmetry : PreservesLimit (cospan g f) G where
+def preservesPullbackSymmetry : PreservesLimit (cospan g f) G where
preserves {c} hc := by
apply (IsLimit.postcomposeHomEquiv (diagramIsoCospan.{v₂} _) _).toFun
apply IsLimit.ofIsoLimit _ (PullbackCone.isoMk _).symm
@@ -177,7 +177,7 @@ def isColimitPushoutCoconeMapOfIsColimit [PreservesColimit (span f g) G]
/-- The property of reflecting pushouts expressed in terms of binary cofans. -/
def isColimitOfIsColimitPushoutCoconeMap [ReflectsColimit (span f g) G]
- (l : IsColimit (PushoutCocone.mk (G.map h) (G.map k) (show G.map f ≫ G.map h =
+ (l : IsColimit (PushoutCocone.mk (G.map h) (G.map k) (show G.map f ≫ G.map h =
G.map g ≫ G.map k from by simp only [←G.map_comp,comm]))) :
IsColimit (PushoutCocone.mk h k comm) :=
ReflectsColimit.reflects ((isColimitMapCoconePushoutCoconeEquiv G comm).symm l)
@@ -188,14 +188,14 @@ variable (f g) [PreservesColimit (span f g) G]
/-- If `G` preserves pushouts and `C` has them, then the pushout cocone constructed of the mapped
morphisms of the pushout cocone is a colimit. -/
def isColimitOfHasPushoutOfPreservesColimit [i : HasPushout f g] :
- IsColimit (PushoutCocone.mk (G.map pushout.inl) (G.map (@pushout.inr _ _ _ _ _ f g i))
- (show G.map f ≫ G.map pushout.inl = G.map g ≫ G.map pushout.inr from by
+ IsColimit (PushoutCocone.mk (G.map pushout.inl) (G.map (@pushout.inr _ _ _ _ _ f g i))
+ (show G.map f ≫ G.map pushout.inl = G.map g ≫ G.map pushout.inr from by
simp only [← G.map_comp, pushout.condition])) :=
isColimitPushoutCoconeMapOfIsColimit G _ (pushoutIsPushout f g)
#align category_theory.limits.is_colimit_of_has_pushout_of_preserves_colimit CategoryTheory.Limits.isColimitOfHasPushoutOfPreservesColimit
/-- If `F` preserves the pushout of `f, g`, it also preserves the pushout of `g, f`. -/
-def preservesPushoutSymmetry : PreservesColimit (span g f) G where
+def preservesPushoutSymmetry : PreservesColimit (span g f) G where
preserves {c} hc :=
by
apply (IsColimit.precomposeHomEquiv (diagramIsoSpan.{v₂} _).symm _).toFun
@@ -322,4 +322,3 @@ end Pushout
end
end CategoryTheory.Limits
-
All dependencies are ported!