category_theory.functor.const ⟷ Mathlib.CategoryTheory.Functor.Const

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

@@ -118,7 +118,7 @@ def constComp (X : C) (F : C ⥤ D) : (const J).obj X ⋙ F ≅ (const J).obj (F
 -/
 
 /-- If `J` is nonempty, then the constant functor over `J` is faithful. -/
-instance [Nonempty J] : Faithful (const J : C ⥤ J ⥤ C)
+instance [Nonempty J] : CategoryTheory.Functor.Faithful (const J : C ⥤ J ⥤ C)
     where map_injective' X Y f g e := NatTrans.congr_app e (Classical.arbitrary J)
 
 end

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

@@ -3,7 +3,7 @@ Copyright (c) 2018 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta
 -/
-import Mathbin.CategoryTheory.Opposites
+import CategoryTheory.Opposites
 
 #align_import category_theory.functor.const from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.functor.const
-! leanprover-community/mathlib commit 34ee86e6a59d911a8e4f89b68793ee7577ae79c7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Opposites
 
+#align_import category_theory.functor.const from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
+
 /-!
 # The constant functor
 

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

@@ -55,6 +55,7 @@ open Opposite
 
 variable {J}
 
+#print CategoryTheory.Functor.const.opObjOp /-
 /-- The contant functor `Jᵒᵖ ⥤ Cᵒᵖ` sending everything to `op X`
 is (naturally isomorphic to) the opposite of the constant functor `J ⥤ C` sending everything to `X`.
 -/
@@ -64,7 +65,9 @@ def opObjOp (X : C) : (const Jᵒᵖ).obj (op X) ≅ ((const J).obj X).op
   Hom := { app := fun j => 𝟙 _ }
   inv := { app := fun j => 𝟙 _ }
 #align category_theory.functor.const.op_obj_op CategoryTheory.Functor.const.opObjOp
+-/
 
+#print CategoryTheory.Functor.const.opObjUnop /-
 /-- The contant functor `Jᵒᵖ ⥤ C` sending everything to `unop X`
 is (naturally isomorphic to) the opposite of
 the constant functor `J ⥤ Cᵒᵖ` sending everything to `X`.
@@ -74,23 +77,30 @@ def opObjUnop (X : Cᵒᵖ) : (const Jᵒᵖ).obj (unop X) ≅ ((const J).obj X)
   Hom := { app := fun j => 𝟙 _ }
   inv := { app := fun j => 𝟙 _ }
 #align category_theory.functor.const.op_obj_unop CategoryTheory.Functor.const.opObjUnop
+-/
 
+#print CategoryTheory.Functor.const.opObjUnop_hom_app /-
 -- Lean needs some help with universes here.
 @[simp]
 theorem opObjUnop_hom_app (X : Cᵒᵖ) (j : Jᵒᵖ) : (opObjUnop.{v₁, v₂} X).Hom.app j = 𝟙 _ :=
   rfl
 #align category_theory.functor.const.op_obj_unop_hom_app CategoryTheory.Functor.const.opObjUnop_hom_app
+-/
 
+#print CategoryTheory.Functor.const.opObjUnop_inv_app /-
 @[simp]
 theorem opObjUnop_inv_app (X : Cᵒᵖ) (j : Jᵒᵖ) : (opObjUnop.{v₁, v₂} X).inv.app j = 𝟙 _ :=
   rfl
 #align category_theory.functor.const.op_obj_unop_inv_app CategoryTheory.Functor.const.opObjUnop_inv_app
+-/
 
+#print CategoryTheory.Functor.const.unop_functor_op_obj_map /-
 @[simp]
 theorem unop_functor_op_obj_map (X : Cᵒᵖ) {j₁ j₂ : J} (f : j₁ ⟶ j₂) :
     (unop ((Functor.op (const J)).obj X)).map f = 𝟙 (unop X) :=
   rfl
 #align category_theory.functor.const.unop_functor_op_obj_map CategoryTheory.Functor.const.unop_functor_op_obj_map
+-/
 
 end Const
 
@@ -98,6 +108,7 @@ section
 
 variable {D : Type u₃} [Category.{v₃} D]
 
+#print CategoryTheory.Functor.constComp /-
 /-- These are actually equal, of course, but not definitionally equal
   (the equality requires F.map (𝟙 _) = 𝟙 _). A natural isomorphism is
   more convenient than an equality between functors (compare id_to_iso). -/
@@ -107,6 +118,7 @@ def constComp (X : C) (F : C ⥤ D) : (const J).obj X ⋙ F ≅ (const J).obj (F
   Hom := { app := fun _ => 𝟙 _ }
   inv := { app := fun _ => 𝟙 _ }
 #align category_theory.functor.const_comp CategoryTheory.Functor.constComp
+-/
 
 /-- If `J` is nonempty, then the constant functor over `J` is faithful. -/
 instance [Nonempty J] : Faithful (const J : C ⥤ J ⥤ C)

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

@@ -55,12 +55,6 @@ open Opposite
 
 variable {J}
 
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 /-- The contant functor `Jᵒᵖ ⥤ Cᵒᵖ` sending everything to `op X`
 is (naturally isomorphic to) the opposite of the constant functor `J ⥤ C` sending everything to `X`.
 -/
@@ -71,12 +65,6 @@ def opObjOp (X : C) : (const Jᵒᵖ).obj (op X) ≅ ((const J).obj X).op
   inv := { app := fun j => 𝟙 _ }
 #align category_theory.functor.const.op_obj_op CategoryTheory.Functor.const.opObjOp
 
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 /-- The contant functor `Jᵒᵖ ⥤ C` sending everything to `unop X`
 is (naturally isomorphic to) the opposite of
 the constant functor `J ⥤ Cᵒᵖ` sending everything to `X`.
@@ -87,26 +75,17 @@ def opObjUnop (X : Cᵒᵖ) : (const Jᵒᵖ).obj (unop X) ≅ ((const J).obj X)
   inv := { app := fun j => 𝟙 _ }
 #align category_theory.functor.const.op_obj_unop CategoryTheory.Functor.const.opObjUnop
 
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-<too large>
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 -- Lean needs some help with universes here.
 @[simp]
 theorem opObjUnop_hom_app (X : Cᵒᵖ) (j : Jᵒᵖ) : (opObjUnop.{v₁, v₂} X).Hom.app j = 𝟙 _ :=
   rfl
 #align category_theory.functor.const.op_obj_unop_hom_app CategoryTheory.Functor.const.opObjUnop_hom_app
 
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-<too large>
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 @[simp]
 theorem opObjUnop_inv_app (X : Cᵒᵖ) (j : Jᵒᵖ) : (opObjUnop.{v₁, v₂} X).inv.app j = 𝟙 _ :=
   rfl
 #align category_theory.functor.const.op_obj_unop_inv_app CategoryTheory.Functor.const.opObjUnop_inv_app
 
-/- warning: category_theory.functor.const.unop_functor_op_obj_map -> CategoryTheory.Functor.const.unop_functor_op_obj_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.const.unop_functor_op_obj_map CategoryTheory.Functor.const.unop_functor_op_obj_mapₓ'. -/
 @[simp]
 theorem unop_functor_op_obj_map (X : Cᵒᵖ) {j₁ j₂ : J} (f : j₁ ⟶ j₂) :
     (unop ((Functor.op (const J)).obj X)).map f = 𝟙 (unop X) :=
@@ -119,12 +98,6 @@ section
 
 variable {D : Type u₃} [Category.{v₃} D]
 
-/- warning: category_theory.functor.const_comp -> CategoryTheory.Functor.constComp is a dubious translation:
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 /-- These are actually equal, of course, but not definitionally equal
   (the equality requires F.map (𝟙 _) = 𝟙 _). A natural isomorphism is
   more convenient than an equality between functors (compare id_to_iso). -/

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

@@ -88,10 +88,7 @@ def opObjUnop (X : Cᵒᵖ) : (const Jᵒᵖ).obj (unop X) ≅ ((const J).obj X)
 #align category_theory.functor.const.op_obj_unop CategoryTheory.Functor.const.opObjUnop
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.functor.const.op_obj_unop_hom_app CategoryTheory.Functor.const.opObjUnop_hom_appₓ'. -/
 -- Lean needs some help with universes here.
 @[simp]
@@ -100,10 +97,7 @@ theorem opObjUnop_hom_app (X : Cᵒᵖ) (j : Jᵒᵖ) : (opObjUnop.{v₁, v₂}
 #align category_theory.functor.const.op_obj_unop_hom_app CategoryTheory.Functor.const.opObjUnop_hom_app
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.functor.const.op_obj_unop_inv_app CategoryTheory.Functor.const.opObjUnop_inv_appₓ'. -/
 @[simp]
 theorem opObjUnop_inv_app (X : Cᵒᵖ) (j : Jᵒᵖ) : (opObjUnop.{v₁, v₂} X).inv.app j = 𝟙 _ :=
@@ -111,10 +105,7 @@ theorem opObjUnop_inv_app (X : Cᵒᵖ) (j : Jᵒᵖ) : (opObjUnop.{v₁, v₂}
 #align category_theory.functor.const.op_obj_unop_inv_app CategoryTheory.Functor.const.opObjUnop_inv_app
 
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_inst_2) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_2)) (CategoryTheory.Functor.op.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_2 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_2) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_2) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_2))) X))) j₁ j₂ f) (CategoryTheory.CategoryStruct.id.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_2) (Opposite.unop.{succ u4} C X))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.const.unop_functor_op_obj_map CategoryTheory.Functor.const.unop_functor_op_obj_mapₓ'. -/
 @[simp]
 theorem unop_functor_op_obj_map (X : Cᵒᵖ) {j₁ j₂ : J} (f : j₁ ⟶ j₂) :

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)

@@ -27,7 +27,6 @@ open CategoryTheory
 namespace CategoryTheory.Functor
 
 variable (J : Type u₁) [Category.{v₁} J]
-
 variable {C : Type u₂} [Category.{v₂} C]
 
 /-- The functor sending `X : C` to the constant functor `J ⥤ C` sending everything to `X`.

This PR contains various prerequisites in order to show that under suitable assumptions, a localized category of a category that has finite products also has finite products:

• the equivalence of categories (J → C) ≌ (Discrete J ⥤ C)
• more API for the existence of limits as a consequence of a right adjoint to the constant functor C ⥤ (J ⥤ C).
• the typeclass MorphismProperty.IsStableUnderFiniteProducts

@@ -104,6 +104,15 @@ def constComp (X : C) (F : C ⥤ D) : (const J).obj X ⋙ F ≅ (const J).obj (F
 instance [Nonempty J] : Faithful (const J : C ⥤ J ⥤ C) where
   map_injective e := NatTrans.congr_app e (Classical.arbitrary J)
 
+/-- The canonical isomorphism
+`F ⋙ Functor.const J ≅ Functor.const F ⋙ (whiskeringRight J _ _).obj L`. -/
+@[simps!]
+def compConstIso (F : C ⥤ D) :
+    F ⋙ Functor.const J ≅ Functor.const J ⋙ (whiskeringRight J C D).obj F :=
+  NatIso.ofComponents
+    (fun X => NatIso.ofComponents (fun j => Iso.refl _) (by aesop_cat))
+    (by aesop_cat)
+
 end
 
 end CategoryTheory.Functor

@@ -101,8 +101,8 @@ def constComp (X : C) (F : C ⥤ D) : (const J).obj X ⋙ F ≅ (const J).obj (F
 #align category_theory.functor.const_comp CategoryTheory.Functor.constComp
 
 /-- If `J` is nonempty, then the constant functor over `J` is faithful. -/
-instance [Nonempty J] : Faithful (const J : C ⥤ J ⥤ C)
-    where map_injective e := NatTrans.congr_app e (Classical.arbitrary J)
+instance [Nonempty J] : Faithful (const J : C ⥤ J ⥤ C) where
+  map_injective e := NatTrans.congr_app e (Classical.arbitrary J)
 
 end
 

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.functor.const
-! leanprover-community/mathlib commit dc6c365e751e34d100e80fe6e314c3c3e0fd2988
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Opposites
 
+#align_import category_theory.functor.const from "leanprover-community/mathlib"@"dc6c365e751e34d100e80fe6e314c3c3e0fd2988"
+
 /-!
 # The constant functor
 

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

@@ -50,7 +50,7 @@ open Opposite
 
 variable {J}
 
-/-- The contant functor `Jᵒᵖ ⥤ Cᵒᵖ` sending everything to `op X`
+/-- The constant functor `Jᵒᵖ ⥤ Cᵒᵖ` sending everything to `op X`
 is (naturally isomorphic to) the opposite of the constant functor `J ⥤ C` sending everything to `X`.
 -/
 @[simps]
@@ -60,7 +60,7 @@ def opObjOp (X : C) : (const Jᵒᵖ).obj (op X) ≅ ((const J).obj X).op
   inv := { app := fun j => 𝟙 _ }
 #align category_theory.functor.const.op_obj_op CategoryTheory.Functor.const.opObjOp
 
-/-- The contant functor `Jᵒᵖ ⥤ C` sending everything to `unop X`
+/-- The constant functor `Jᵒᵖ ⥤ C` sending everything to `unop X`
 is (naturally isomorphic to) the opposite of
 the constant functor `J ⥤ Cᵒᵖ` sending everything to `X`.
 -/

Very straightforward port. Almost completely automatic!