category_theory.monoidal.internal.limits
⟷
Mathlib.CategoryTheory.Monoidal.Internal.Limits
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
@@ -3,9 +3,9 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathbin.CategoryTheory.Monoidal.Internal.FunctorCategory
-import Mathbin.CategoryTheory.Monoidal.Limits
-import Mathbin.CategoryTheory.Limits.Preserves.Basic
+import CategoryTheory.Monoidal.Internal.FunctorCategory
+import CategoryTheory.Monoidal.Limits
+import CategoryTheory.Limits.Preserves.Basic
#align_import category_theory.monoidal.internal.limits from "leanprover-community/mathlib"@"e160cefedc932ce41c7049bf0c4b0f061d06216e"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.monoidal.internal.limits
-! leanprover-community/mathlib commit e160cefedc932ce41c7049bf0c4b0f061d06216e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Monoidal.Internal.FunctorCategory
import Mathbin.CategoryTheory.Monoidal.Limits
import Mathbin.CategoryTheory.Limits.Preserves.Basic
+#align_import category_theory.monoidal.internal.limits from "leanprover-community/mathlib"@"e160cefedc932ce41c7049bf0c4b0f061d06216e"
+
/-!
# Limits of monoid objects.
mathlib commit https://github.com/leanprover-community/mathlib/commit/0723536a0522d24fc2f159a096fb3304bef77472
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
! This file was ported from Lean 3 source module category_theory.monoidal.internal.limits
-! leanprover-community/mathlib commit 12921e9eaa574d0087ae4856860e6dda8690a438
+! leanprover-community/mathlib commit e160cefedc932ce41c7049bf0c4b0f061d06216e
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Limits.Preserves.Basic
/-!
# Limits of monoid objects.
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
If `C` has limits, so does `Mon_ C`, and the forgetful functor preserves these limits.
(This could potentially replace many individual constructions for concrete categories,
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -38,6 +38,7 @@ variable {J : Type v} [SmallCategory J]
variable {C : Type u} [Category.{v} C] [HasLimits C] [MonoidalCategory.{v} C]
+#print Mon_.limit /-
/-- We construct the (candidate) limit of a functor `F : J ⥤ Mon_ C`
by interpreting it as a functor `Mon_ (J ⥤ C)`,
and noting that taking limits is a lax monoidal functor,
@@ -47,7 +48,9 @@ and hence sends monoid objects to monoid objects.
def limit (F : J ⥤ Mon_ C) : Mon_ C :=
limLax.mapMon.obj (MonFunctorCategoryEquivalence.inverse.obj F)
#align Mon_.limit Mon_.limit
+-/
+#print Mon_.limitCone /-
/-- Implementation of `Mon_.has_limits`: a limiting cone over a functor `F : J ⥤ Mon_ C`.
-/
@[simps]
@@ -57,7 +60,9 @@ def limitCone (F : J ⥤ Mon_ C) : Cone F where
{ app := fun j => { Hom := limit.π (F ⋙ Mon_.forget C) j }
naturality' := fun j j' f => by ext; exact (limit.cone (F ⋙ Mon_.forget C)).π.naturality f }
#align Mon_.limit_cone Mon_.limitCone
+-/
+#print Mon_.forgetMapConeLimitConeIso /-
/-- The image of the proposed limit cone for `F : J ⥤ Mon_ C` under the forgetful functor
`forget C : Mon_ C ⥤ C` is isomorphic to the limit cone of `F ⋙ forget C`.
-/
@@ -65,7 +70,9 @@ def forgetMapConeLimitConeIso (F : J ⥤ Mon_ C) :
(forget C).mapCone (limitCone F) ≅ limit.cone (F ⋙ forget C) :=
Cones.ext (Iso.refl _) fun j => by tidy
#align Mon_.forget_map_cone_limit_cone_iso Mon_.forgetMapConeLimitConeIso
+-/
+#print Mon_.limitConeIsLimit /-
/-- Implementation of `Mon_.has_limits`:
the proposed cone over a functor `F : J ⥤ Mon_ C` is a limit cone.
-/
@@ -85,7 +92,9 @@ def limitConeIsLimit (F : J ⥤ Mon_ C) : IsLimit (limitCone F)
dsimp; simp only [Mon_.forget_map, limit.lift_π, functor.map_cone_π_app]
exact congr_arg Mon_.Hom.hom (w j)
#align Mon_.limit_cone_is_limit Mon_.limitConeIsLimit
+-/
+#print Mon_.hasLimits /-
instance hasLimits : HasLimits (Mon_ C)
where HasLimitsOfShape J 𝒥 :=
{
@@ -94,7 +103,9 @@ instance hasLimits : HasLimits (Mon_ C)
{ Cone := limit_cone F
IsLimit := limit_cone_is_limit F } }
#align Mon_.has_limits Mon_.hasLimits
+-/
+#print Mon_.forgetPreservesLimits /-
instance forgetPreservesLimits : PreservesLimits (Mon_.forget C)
where PreservesLimitsOfShape J 𝒥 :=
{
@@ -103,6 +114,7 @@ instance forgetPreservesLimits : PreservesLimits (Mon_.forget C)
(is_limit.of_iso_limit (limit.is_limit (F ⋙ Mon_.forget C))
(forget_map_cone_limit_cone_iso F).symm) }
#align Mon_.forget_preserves_limits Mon_.forgetPreservesLimits
+-/
end Mon_
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -55,9 +55,7 @@ def limitCone (F : J ⥤ Mon_ C) : Cone F where
pt := limit F
π :=
{ app := fun j => { Hom := limit.π (F ⋙ Mon_.forget C) j }
- naturality' := fun j j' f => by
- ext
- exact (limit.cone (F ⋙ Mon_.forget C)).π.naturality f }
+ naturality' := fun j j' f => by ext; exact (limit.cone (F ⋙ Mon_.forget C)).π.naturality f }
#align Mon_.limit_cone Mon_.limitCone
/-- The image of the proposed limit cone for `F : J ⥤ Mon_ C` under the forgetful functor
@@ -81,9 +79,7 @@ def limitConeIsLimit (F : J ⥤ Mon_ C) : IsLimit (limitCone F)
slice_rhs 1 2 =>
rw [← monoidal_category.tensor_comp, limit.lift_π]
dsimp }
- fac s h := by
- ext
- simp
+ fac s h := by ext; simp
uniq s m w := by
ext
dsimp; simp only [Mon_.forget_map, limit.lift_π, functor.map_cone_π_app]
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -52,7 +52,7 @@ def limit (F : J ⥤ Mon_ C) : Mon_ C :=
-/
@[simps]
def limitCone (F : J ⥤ Mon_ C) : Cone F where
- x := limit F
+ pt := limit F
π :=
{ app := fun j => { Hom := limit.π (F ⋙ Mon_.forget C) j }
naturality' := fun j j' f => by
@@ -64,7 +64,7 @@ def limitCone (F : J ⥤ Mon_ C) : Cone F where
`forget C : Mon_ C ⥤ C` is isomorphic to the limit cone of `F ⋙ forget C`.
-/
def forgetMapConeLimitConeIso (F : J ⥤ Mon_ C) :
- (forget C).mapCone (limitCone F) ≅ Limit.cone (F ⋙ forget C) :=
+ (forget C).mapCone (limitCone F) ≅ limit.cone (F ⋙ forget C) :=
Cones.ext (Iso.refl _) fun j => by tidy
#align Mon_.forget_map_cone_limit_cone_iso Mon_.forgetMapConeLimitConeIso
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -81,10 +81,10 @@ def limitConeIsLimit (F : J ⥤ Mon_ C) : IsLimit (limitCone F)
slice_rhs 1 2 =>
rw [← monoidal_category.tensor_comp, limit.lift_π]
dsimp }
- fac' s h := by
+ fac s h := by
ext
simp
- uniq' s m w := by
+ uniq s m w := by
ext
dsimp; simp only [Mon_.forget_map, limit.lift_π, functor.map_cone_π_app]
exact congr_arg Mon_.Hom.hom (w j)
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)
@@ -28,7 +28,6 @@ noncomputable section
namespace Mon_
variable {J : Type v} [SmallCategory J]
-
variable {C : Type u} [Category.{v} C] [HasLimits C] [MonoidalCategory.{v} C]
/-- We construct the (candidate) limit of a functor `F : J ⥤ Mon_ C`
@@ -15,7 +15,7 @@ import Mathlib.CategoryTheory.Limits.Preserves.Basic
If `C` has limits, so does `Mon_ C`, and the forgetful functor preserves these limits.
(This could potentially replace many individual constructions for concrete categories,
-in particular `Mon`, `SemiRing`, `Ring`, and `Algebra R`.)
+in particular `MonCat`, `SemiRingCat`, `RingCat`, and `AlgebraCat R`.)
-/
@@ -71,7 +71,11 @@ def limitConeIsLimit (F : J ⥤ Mon_ C) : IsLimit (limitCone F) where
{ hom := limit.lift (F ⋙ Mon_.forget C) ((Mon_.forget C).mapCone s)
mul_hom := by
dsimp
- ext; simp
+ ext
+ simp only [Functor.comp_obj, forget_obj, Category.assoc, limit.lift_π, Functor.mapCone_pt,
+ Functor.mapCone_π_app, forget_map, Hom.mul_hom, limit_mul, Cones.postcompose_obj_pt,
+ Cones.postcompose_obj_π, NatTrans.comp_app, Functor.const_obj_obj, tensorObj_obj,
+ MonFunctorCategoryEquivalence.Inverse.obj_mul_app]
slice_rhs 1 2 => rw [← MonoidalCategory.tensor_comp, limit.lift_π] }
fac s h := by ext; simp
uniq s m w := by
@@ -82,8 +86,8 @@ def limitConeIsLimit (F : J ⥤ Mon_ C) : IsLimit (limitCone F) where
set_option linter.uppercaseLean3 false in
#align Mon_.limit_cone_is_limit Mon_.limitConeIsLimit
-instance hasLimits : HasLimits (Mon_ C)
- where has_limits_of_shape _ _ :=
+instance hasLimits : HasLimits (Mon_ C) where
+ has_limits_of_shape _ _ :=
{ has_limit := fun F =>
HasLimit.mk
{ cone := limitCone F
@@ -71,9 +71,8 @@ def limitConeIsLimit (F : J ⥤ Mon_ C) : IsLimit (limitCone F) where
{ hom := limit.lift (F ⋙ Mon_.forget C) ((Mon_.forget C).mapCone s)
mul_hom := by
dsimp
- ext; simp; dsimp
- slice_rhs 1 2 =>
- rw [← MonoidalCategory.tensor_comp, limit.lift_π] }
+ ext; simp
+ slice_rhs 1 2 => rw [← MonoidalCategory.tensor_comp, limit.lift_π] }
fac s h := by ext; simp
uniq s m w := by
ext1
@@ -2,16 +2,13 @@
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.monoidal.internal.limits
-! leanprover-community/mathlib commit 12921e9eaa574d0087ae4856860e6dda8690a438
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory
import Mathlib.CategoryTheory.Monoidal.Limits
import Mathlib.CategoryTheory.Limits.Preserves.Basic
+#align_import category_theory.monoidal.internal.limits from "leanprover-community/mathlib"@"12921e9eaa574d0087ae4856860e6dda8690a438"
+
/-!
# Limits of monoid objects.
The unported dependencies are