category_theory.closed.functorMathlib.CategoryTheory.Closed.Functor

This file has been ported!

Changes since the initial port

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

Changes in mathlib3

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -73,8 +73,8 @@ def frobeniusMorphism (h : L ⊣ F) (A : C) :
 Frobenius morphism is an isomorphism.
 -/
 instance frobeniusMorphism_iso_of_preserves_binary_products (h : L ⊣ F) (A : C)
-    [PreservesLimitsOfShape (Discrete WalkingPair) L] [Full F] [Faithful F] :
-    IsIso (frobeniusMorphism F h A) :=
+    [PreservesLimitsOfShape (Discrete WalkingPair) L] [CategoryTheory.Functor.Full F]
+    [CategoryTheory.Functor.Faithful F] : IsIso (frobeniusMorphism F h A) :=
   by
   apply nat_iso.is_iso_of_is_iso_app _
   intro B
@@ -206,7 +206,8 @@ cartesian closed.
 TODO: Show the converse, that if `F` is cartesian closed and its left adjoint preserves binary
 products, then it is full and faithful.
 -/
-def cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts (h : L ⊣ F) [Full F] [Faithful F]
+def cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts (h : L ⊣ F)
+    [CategoryTheory.Functor.Full F] [CategoryTheory.Functor.Faithful F]
     [PreservesLimitsOfShape (Discrete WalkingPair) L] : CartesianClosedFunctor F
     where comparison_iso A := expComparison_iso_of_frobeniusMorphism_iso F h _
 #align category_theory.cartesian_closed_functor_of_left_adjoint_preserves_binary_products CategoryTheory.cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts
Diff
@@ -183,7 +183,7 @@ at `A` is an isomorphism.
 theorem frobeniusMorphism_iso_of_expComparison_iso (h : L ⊣ F) (A : C)
     [i : IsIso (expComparison F A)] : IsIso (frobeniusMorphism F h A) :=
   by
-  rw [← frobenius_morphism_mate F h] at i 
+  rw [← frobenius_morphism_mate F h] at i
   exact @transfer_nat_trans_self_of_iso _ _ _ _ _ i
 #align category_theory.frobenius_morphism_iso_of_exp_comparison_iso CategoryTheory.frobeniusMorphism_iso_of_expComparison_iso
 -/
Diff
@@ -3,9 +3,9 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 -/
-import Mathbin.CategoryTheory.Closed.Cartesian
-import Mathbin.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
-import Mathbin.CategoryTheory.Adjunction.FullyFaithful
+import CategoryTheory.Closed.Cartesian
+import CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
+import CategoryTheory.Adjunction.FullyFaithful
 
 #align_import category_theory.closed.functor from "leanprover-community/mathlib"@"cff8231f04dfa33fd8f2f45792eebd862ef30cad"
 
Diff
@@ -2,16 +2,13 @@
 Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.closed.functor
-! leanprover-community/mathlib commit cff8231f04dfa33fd8f2f45792eebd862ef30cad
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Closed.Cartesian
 import Mathbin.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
 import Mathbin.CategoryTheory.Adjunction.FullyFaithful
 
+#align_import category_theory.closed.functor from "leanprover-community/mathlib"@"cff8231f04dfa33fd8f2f45792eebd862ef30cad"
+
 /-!
 # Cartesian closed functors
 
Diff
@@ -54,6 +54,7 @@ variable (F : C ⥤ D) {L : D ⥤ C}
 
 noncomputable section
 
+#print CategoryTheory.frobeniusMorphism /-
 /-- The Frobenius morphism for an adjunction `L ⊣ F` at `A` is given by the morphism
 
     L(FA ⨯ B) ⟶ LFA ⨯ LB ⟶ A ⨯ LB
@@ -68,7 +69,9 @@ def frobeniusMorphism (h : L ⊣ F) (A : C) :
     prod.functor.obj (F.obj A) ⋙ L ⟶ L ⋙ prod.functor.obj A :=
   prodComparisonNatTrans L (F.obj A) ≫ whiskerLeft _ (prod.functor.map (h.counit.app _))
 #align category_theory.frobenius_morphism CategoryTheory.frobeniusMorphism
+-/
 
+#print CategoryTheory.frobeniusMorphism_iso_of_preserves_binary_products /-
 /-- If `F` is full and faithful and has a left adjoint `L` which preserves binary products, then the
 Frobenius morphism is an isomorphism.
 -/
@@ -81,18 +84,22 @@ instance frobeniusMorphism_iso_of_preserves_binary_products (h : L ⊣ F) (A : C
   dsimp [frobenius_morphism]
   infer_instance
 #align category_theory.frobenius_morphism_iso_of_preserves_binary_products CategoryTheory.frobeniusMorphism_iso_of_preserves_binary_products
+-/
 
 variable [CartesianClosed C] [CartesianClosed D]
 
 variable [PreservesLimitsOfShape (Discrete WalkingPair) F]
 
+#print CategoryTheory.expComparison /-
 /-- The exponential comparison map.
 `F` is a cartesian closed functor if this is an iso for all `A`.
 -/
 def expComparison (A : C) : exp A ⋙ F ⟶ F ⋙ exp (F.obj A) :=
   transferNatTrans (exp.adjunction A) (exp.adjunction (F.obj A)) (prodComparisonNatIso F A).inv
 #align category_theory.exp_comparison CategoryTheory.expComparison
+-/
 
+#print CategoryTheory.expComparison_ev /-
 theorem expComparison_ev (A B : C) :
     Limits.prod.map (𝟙 (F.obj A)) ((expComparison F A).app B) ≫ (exp.ev (F.obj A)).app (F.obj B) =
       inv (prodComparison F _ _) ≫ F.map ((exp.ev _).app _) :=
@@ -101,7 +108,9 @@ theorem expComparison_ev (A B : C) :
   ext
   simp
 #align category_theory.exp_comparison_ev CategoryTheory.expComparison_ev
+-/
 
+#print CategoryTheory.coev_expComparison /-
 theorem coev_expComparison (A B : C) :
     F.map ((exp.coev A).app B) ≫ (expComparison F A).app (A ⨯ B) =
       (exp.coev _).app (F.obj B) ≫ (exp (F.obj A)).map (inv (prodComparison F A B)) :=
@@ -111,13 +120,17 @@ theorem coev_expComparison (A B : C) :
   dsimp
   simp
 #align category_theory.coev_exp_comparison CategoryTheory.coev_expComparison
+-/
 
+#print CategoryTheory.uncurry_expComparison /-
 theorem uncurry_expComparison (A B : C) :
     CartesianClosed.uncurry ((expComparison F A).app B) =
       inv (prodComparison F _ _) ≫ F.map ((exp.ev _).app _) :=
   by rw [uncurry_eq, exp_comparison_ev]
 #align category_theory.uncurry_exp_comparison CategoryTheory.uncurry_expComparison
+-/
 
+#print CategoryTheory.expComparison_whiskerLeft /-
 /-- The exponential comparison map is natural in `A`. -/
 theorem expComparison_whiskerLeft {A A' : C} (f : A' ⟶ A) :
     expComparison F A ≫ whiskerLeft _ (pre (F.map f)) =
@@ -131,16 +144,20 @@ theorem expComparison_whiskerLeft {A A' : C} (f : A' ⟶ A) :
     prod_comparison_inv_natural_assoc, ← prod_comparison_inv_natural_assoc, ← F.map_comp, ←
     F.map_comp, prod_map_pre_app_comp_ev]
 #align category_theory.exp_comparison_whisker_left CategoryTheory.expComparison_whiskerLeft
+-/
 
+#print CategoryTheory.CartesianClosedFunctor /-
 /-- The functor `F` is cartesian closed (ie preserves exponentials) if each natural transformation
 `exp_comparison F A` is an isomorphism
 -/
 class CartesianClosedFunctor where
   comparison_iso : ∀ A, IsIso (expComparison F A)
 #align category_theory.cartesian_closed_functor CategoryTheory.CartesianClosedFunctor
+-/
 
 attribute [instance] cartesian_closed_functor.comparison_iso
 
+#print CategoryTheory.frobeniusMorphism_mate /-
 theorem frobeniusMorphism_mate (h : L ⊣ F) (A : C) :
     transferNatTransSelf (h.comp (exp.adjunction A)) ((exp.adjunction (F.obj A)).comp h)
         (frobeniusMorphism F h A) =
@@ -159,7 +176,9 @@ theorem frobeniusMorphism_mate (h : L ⊣ F) (A : C) :
   · rw [assoc, assoc, ← h.counit_naturality, ← L.map_comp_assoc, assoc, inv_prod_comparison_map_snd]
     simp
 #align category_theory.frobenius_morphism_mate CategoryTheory.frobeniusMorphism_mate
+-/
 
+#print CategoryTheory.frobeniusMorphism_iso_of_expComparison_iso /-
 /--
 If the exponential comparison transformation (at `A`) is an isomorphism, then the Frobenius morphism
 at `A` is an isomorphism.
@@ -170,7 +189,9 @@ theorem frobeniusMorphism_iso_of_expComparison_iso (h : L ⊣ F) (A : C)
   rw [← frobenius_morphism_mate F h] at i 
   exact @transfer_nat_trans_self_of_iso _ _ _ _ _ i
 #align category_theory.frobenius_morphism_iso_of_exp_comparison_iso CategoryTheory.frobeniusMorphism_iso_of_expComparison_iso
+-/
 
+#print CategoryTheory.expComparison_iso_of_frobeniusMorphism_iso /-
 /--
 If the Frobenius morphism at `A` is an isomorphism, then the exponential comparison transformation
 (at `A`) is an isomorphism.
@@ -179,7 +200,9 @@ theorem expComparison_iso_of_frobeniusMorphism_iso (h : L ⊣ F) (A : C)
     [i : IsIso (frobeniusMorphism F h A)] : IsIso (expComparison F A) := by
   rw [← frobenius_morphism_mate F h]; infer_instance
 #align category_theory.exp_comparison_iso_of_frobenius_morphism_iso CategoryTheory.expComparison_iso_of_frobeniusMorphism_iso
+-/
 
+#print CategoryTheory.cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts /-
 /-- If `F` is full and faithful, and has a left adjoint which preserves binary products, then it is
 cartesian closed.
 
@@ -190,6 +213,7 @@ def cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts (h : L ⊣ F) [Fu
     [PreservesLimitsOfShape (Discrete WalkingPair) L] : CartesianClosedFunctor F
     where comparison_iso A := expComparison_iso_of_frobeniusMorphism_iso F h _
 #align category_theory.cartesian_closed_functor_of_left_adjoint_preserves_binary_products CategoryTheory.cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts
+-/
 
 end CategoryTheory
 
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 
 ! This file was ported from Lean 3 source module category_theory.closed.functor
-! leanprover-community/mathlib commit cea27692b3fdeb328a2ddba6aabf181754543184
+! leanprover-community/mathlib commit cff8231f04dfa33fd8f2f45792eebd862ef30cad
 ! 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.Adjunction.FullyFaithful
 /-!
 # Cartesian closed functors
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Define the exponential comparison morphisms for a functor which preserves binary products, and use
 them to define a cartesian closed functor: one which (naturally) preserves exponentials.
 
Diff
@@ -164,7 +164,7 @@ at `A` is an isomorphism.
 theorem frobeniusMorphism_iso_of_expComparison_iso (h : L ⊣ F) (A : C)
     [i : IsIso (expComparison F A)] : IsIso (frobeniusMorphism F h A) :=
   by
-  rw [← frobenius_morphism_mate F h] at i
+  rw [← frobenius_morphism_mate F h] at i 
   exact @transfer_nat_trans_self_of_iso _ _ _ _ _ i
 #align category_theory.frobenius_morphism_iso_of_exp_comparison_iso CategoryTheory.frobeniusMorphism_iso_of_expComparison_iso
 
Diff
@@ -173,10 +173,8 @@ If the Frobenius morphism at `A` is an isomorphism, then the exponential compari
 (at `A`) is an isomorphism.
 -/
 theorem expComparison_iso_of_frobeniusMorphism_iso (h : L ⊣ F) (A : C)
-    [i : IsIso (frobeniusMorphism F h A)] : IsIso (expComparison F A) :=
-  by
-  rw [← frobenius_morphism_mate F h]
-  infer_instance
+    [i : IsIso (frobeniusMorphism F h A)] : IsIso (expComparison F A) := by
+  rw [← frobenius_morphism_mate F h]; infer_instance
 #align category_theory.exp_comparison_iso_of_frobenius_morphism_iso CategoryTheory.expComparison_iso_of_frobeniusMorphism_iso
 
 /-- If `F` is full and faithful, and has a left adjoint which preserves binary products, then it is

Changes in mathlib4

mathlib3
mathlib4
chore(CategoryTheory): move Full, Faithful, EssSurj, IsEquivalence and ReflectsIsomorphisms to the Functor namespace (#11985)

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

Diff
@@ -64,7 +64,7 @@ def frobeniusMorphism (h : L ⊣ F) (A : C) :
 Frobenius morphism is an isomorphism.
 -/
 instance frobeniusMorphism_iso_of_preserves_binary_products (h : L ⊣ F) (A : C)
-    [PreservesLimitsOfShape (Discrete WalkingPair) L] [Full F] [Faithful F] :
+    [PreservesLimitsOfShape (Discrete WalkingPair) L] [F.Full] [F.Faithful] :
     IsIso (frobeniusMorphism F h A) :=
   suffices ∀ (X : D), IsIso ((frobeniusMorphism F h A).app X) from NatIso.isIso_of_isIso_app _
   fun B ↦ by dsimp [frobeniusMorphism]; infer_instance
@@ -174,7 +174,7 @@ cartesian closed.
 TODO: Show the converse, that if `F` is cartesian closed and its left adjoint preserves binary
 products, then it is full and faithful.
 -/
-theorem cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts (h : L ⊣ F) [Full F] [Faithful F]
+theorem cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts (h : L ⊣ F) [F.Full] [F.Faithful]
     [PreservesLimitsOfShape (Discrete WalkingPair) L] : CartesianClosedFunctor F where
   comparison_iso _ := expComparison_iso_of_frobeniusMorphism_iso F h _
 #align category_theory.cartesian_closed_functor_of_left_adjoint_preserves_binary_products CategoryTheory.cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts
chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)
Diff
@@ -41,11 +41,8 @@ open Category Limits CartesianClosed
 universe v u u'
 
 variable {C : Type u} [Category.{v} C]
-
 variable {D : Type u'} [Category.{v} D]
-
 variable [HasFiniteProducts C] [HasFiniteProducts D]
-
 variable (F : C ⥤ D) {L : D ⥤ C}
 
 /-- The Frobenius morphism for an adjunction `L ⊣ F` at `A` is given by the morphism
@@ -74,7 +71,6 @@ instance frobeniusMorphism_iso_of_preserves_binary_products (h : L ⊣ F) (A : C
 #align category_theory.frobenius_morphism_iso_of_preserves_binary_products CategoryTheory.frobeniusMorphism_iso_of_preserves_binary_products
 
 variable [CartesianClosed C] [CartesianClosed D]
-
 variable [PreservesLimitsOfShape (Discrete WalkingPair) F]
 
 /-- The exponential comparison map.
feat: Linter that checks that Prop classes are Props (#6148)
Diff
@@ -123,7 +123,7 @@ theorem expComparison_whiskerLeft {A A' : C} (f : A' ⟶ A) :
 /-- The functor `F` is cartesian closed (ie preserves exponentials) if each natural transformation
 `exp_comparison F A` is an isomorphism
 -/
-class CartesianClosedFunctor where
+class CartesianClosedFunctor : Prop where
   comparison_iso : ∀ A, IsIso (expComparison F A)
 #align category_theory.cartesian_closed_functor CategoryTheory.CartesianClosedFunctor
 
@@ -178,7 +178,7 @@ cartesian closed.
 TODO: Show the converse, that if `F` is cartesian closed and its left adjoint preserves binary
 products, then it is full and faithful.
 -/
-def cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts (h : L ⊣ F) [Full F] [Faithful F]
+theorem cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts (h : L ⊣ F) [Full F] [Faithful F]
     [PreservesLimitsOfShape (Discrete WalkingPair) L] : CartesianClosedFunctor F where
   comparison_iso _ := expComparison_iso_of_frobeniusMorphism_iso F h _
 #align category_theory.cartesian_closed_functor_of_left_adjoint_preserves_binary_products CategoryTheory.cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

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

Diff
@@ -2,16 +2,13 @@
 Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.closed.functor
-! leanprover-community/mathlib commit cea27692b3fdeb328a2ddba6aabf181754543184
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Closed.Cartesian
 import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
 import Mathlib.CategoryTheory.Adjunction.FullyFaithful
 
+#align_import category_theory.closed.functor from "leanprover-community/mathlib"@"cea27692b3fdeb328a2ddba6aabf181754543184"
+
 /-!
 # Cartesian closed functors
 
feat: more consistent use of ext, and updating porting notes. (#5242)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

Diff
@@ -149,7 +149,7 @@ theorem frobeniusMorphism_mate (h : L ⊣ F) (A : C) :
   -- https://github.com/leanprover-community/mathlib4/issues/5164
   erw [exp.ev_coev]
   rw [F.map_id (A ⨯ L.obj B), comp_id]
-  apply prod.hom_ext
+  ext
   · rw [assoc, assoc, ← h.counit_naturality, ← L.map_comp_assoc, assoc, inv_prodComparison_map_fst]
     simp
   · rw [assoc, assoc, ← h.counit_naturality, ← L.map_comp_assoc, assoc, inv_prodComparison_map_snd]
chore: add links to issue for rw regressions (#5167)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

Diff
@@ -142,9 +142,11 @@ theorem frobeniusMorphism_mate (h : L ⊣ F) (A : C) :
   simp only [id_comp, comp_id]
   rw [← L.map_comp_assoc, prod.map_id_comp, assoc]
   -- Porting note: need to use `erw` here.
+  -- https://github.com/leanprover-community/mathlib4/issues/5164
   erw [expComparison_ev]
   rw [prod.map_id_comp, assoc, ← F.map_id, ← prodComparison_inv_natural_assoc, ← F.map_comp]
   -- Porting note: need to use `erw` here.
+  -- https://github.com/leanprover-community/mathlib4/issues/5164
   erw [exp.ev_coev]
   rw [F.map_id (A ⨯ L.obj B), comp_id]
   apply prod.hom_ext
feat: port CategoryTheory.Closed.Functor (#4922)

Co-authored-by: int-y1 <jason_yuen2007@hotmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

Dependencies 3 + 263

264 files ported (98.9%)
105692 lines ported (99.8%)
Show graph

The unported dependencies are