category_theory.adjunction.adjoint_functor_theorems
⟷
Mathlib.CategoryTheory.Adjunction.AdjointFunctorTheorems
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
@@ -3,11 +3,11 @@ Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
-import Mathbin.CategoryTheory.Generator
-import Mathbin.CategoryTheory.Limits.ConeCategory
-import Mathbin.CategoryTheory.Limits.Constructions.WeaklyInitial
-import Mathbin.CategoryTheory.Limits.FunctorCategory
-import Mathbin.CategoryTheory.Subobject.Comma
+import CategoryTheory.Generator
+import CategoryTheory.Limits.ConeCategory
+import CategoryTheory.Limits.Constructions.WeaklyInitial
+import CategoryTheory.Limits.FunctorCategory
+import CategoryTheory.Subobject.Comma
#align_import category_theory.adjunction.adjoint_functor_theorems from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,11 +2,6 @@
Copyright (c) 2021 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.adjunction.adjoint_functor_theorems
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Generator
import Mathbin.CategoryTheory.Limits.ConeCategory
@@ -14,6 +9,8 @@ import Mathbin.CategoryTheory.Limits.Constructions.WeaklyInitial
import Mathbin.CategoryTheory.Limits.FunctorCategory
import Mathbin.CategoryTheory.Subobject.Comma
+#align_import category_theory.adjunction.adjoint_functor_theorems from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
/-!
# Adjoint functor theorem
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -64,8 +64,8 @@ adjoint functor theorem to go through.
-/
def SolutionSetCondition {D : Type u} [Category.{v} D] (G : D ⥤ C) : Prop :=
∀ A : C,
- ∃ (ι : Type v)(B : ι → D)(f : ∀ i : ι, A ⟶ G.obj (B i)),
- ∀ (X) (h : A ⟶ G.obj X), ∃ (i : ι)(g : B i ⟶ X), f i ≫ G.map g = h
+ ∃ (ι : Type v) (B : ι → D) (f : ∀ i : ι, A ⟶ G.obj (B i)),
+ ∀ (X) (h : A ⟶ G.obj X), ∃ (i : ι) (g : B i ⟶ X), f i ≫ G.map g = h
#align category_theory.solution_set_condition CategoryTheory.SolutionSetCondition
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780
@@ -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.adjunction.adjoint_functor_theorems
-! leanprover-community/mathlib commit 361aa777b4d262212c31d7c4a245ccb23645c156
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -17,6 +17,9 @@ import Mathbin.CategoryTheory.Subobject.Comma
/-!
# Adjoint functor theorem
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file proves the (general) adjoint functor theorem, in the form:
* If `G : D ⥤ C` preserves limits and `D` has limits, and satisfies the solution set condition,
then it has a left adjoint: `is_right_adjoint_of_preserves_limits_of_solution_set_condition`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c
@@ -50,6 +50,7 @@ variable {J : Type v}
variable {C : Type u} [Category.{v} C]
+#print CategoryTheory.SolutionSetCondition /-
/-- The functor `G : D ⥤ C` satisfies the *solution set condition* if for every `A : C`, there is a
family of morphisms `{f_i : A ⟶ G (B_i) // i ∈ ι}` such that given any morphism `h : A ⟶ G X`,
there is some `i ∈ ι` such that `h` factors through `f_i`.
@@ -63,6 +64,7 @@ def SolutionSetCondition {D : Type u} [Category.{v} D] (G : D ⥤ C) : Prop :=
∃ (ι : Type v)(B : ι → D)(f : ∀ i : ι, A ⟶ G.obj (B i)),
∀ (X) (h : A ⟶ G.obj X), ∃ (i : ι)(g : B i ⟶ X), f i ≫ G.map g = h
#align category_theory.solution_set_condition CategoryTheory.SolutionSetCondition
+-/
section GeneralAdjointFunctorTheorem
@@ -70,6 +72,7 @@ variable {D : Type u} [Category.{v} D]
variable (G : D ⥤ C)
+#print CategoryTheory.solutionSetCondition_of_isRightAdjoint /-
/-- If `G : D ⥤ C` is a right adjoint it satisfies the solution set condition. -/
theorem solutionSetCondition_of_isRightAdjoint [IsRightAdjoint G] : SolutionSetCondition G :=
by
@@ -80,7 +83,9 @@ theorem solutionSetCondition_of_isRightAdjoint [IsRightAdjoint G] : SolutionSetC
refine' ⟨PUnit.unit, ((adjunction.of_right_adjoint G).homEquiv _ _).symm h, _⟩
rw [← adjunction.hom_equiv_unit, Equiv.apply_symm_apply]
#align category_theory.solution_set_condition_of_is_right_adjoint CategoryTheory.solutionSetCondition_of_isRightAdjoint
+-/
+#print CategoryTheory.isRightAdjointOfPreservesLimitsOfSolutionSetCondition /-
/-- The general adjoint functor theorem says that if `G : D ⥤ C` preserves limits and `D` has them,
if `G` satisfies the solution set condition then `G` is a right adjoint.
-/
@@ -100,6 +105,7 @@ noncomputable def isRightAdjointOfPreservesLimitsOfSolutionSetCondition [HasLimi
obtain ⟨T, hT⟩ := has_weakly_initial_of_weakly_initial_set_and_has_products hB'
apply has_initial_of_weakly_initial_and_has_wide_equalizers hT
#align category_theory.is_right_adjoint_of_preserves_limits_of_solution_set_condition CategoryTheory.isRightAdjointOfPreservesLimitsOfSolutionSetCondition
+-/
end GeneralAdjointFunctorTheorem
@@ -107,6 +113,7 @@ section SpecialAdjointFunctorTheorem
variable {D : Type u'} [Category.{v} D]
+#print CategoryTheory.isRightAdjointOfPreservesLimitsOfIsCoseparating /-
/-- The special adjoint functor theorem: if `G : D ⥤ C` preserves limits and `D` is complete,
well-powered and has a small coseparating set, then `G` has a left adjoint.
-/
@@ -117,7 +124,9 @@ noncomputable def isRightAdjointOfPreservesLimitsOfIsCoseparating [HasLimits D]
hasInitial_of_isCoseparating (StructuredArrow.isCoseparating_proj_preimage A G h𝒢)
is_right_adjoint_of_structured_arrow_initials _
#align category_theory.is_right_adjoint_of_preserves_limits_of_is_coseparating CategoryTheory.isRightAdjointOfPreservesLimitsOfIsCoseparating
+-/
+#print CategoryTheory.isLeftAdjointOfPreservesColimitsOfIsSeparatig /-
/-- The special adjoint functor theorem: if `F : C ⥤ D` preserves colimits and `C` is cocomplete,
well-copowered and has a small separating set, then `F` has a right adjoint.
-/
@@ -128,11 +137,13 @@ noncomputable def isLeftAdjointOfPreservesColimitsOfIsSeparatig [HasColimits C]
hasTerminal_of_isSeparating (CostructuredArrow.isSeparating_proj_preimage F A h𝒢)
is_left_adjoint_of_costructured_arrow_terminals _
#align category_theory.is_left_adjoint_of_preserves_colimits_of_is_separatig CategoryTheory.isLeftAdjointOfPreservesColimitsOfIsSeparatig
+-/
end SpecialAdjointFunctorTheorem
namespace Limits
+#print CategoryTheory.Limits.hasColimits_of_hasLimits_of_isCoseparating /-
/-- A consequence of the special adjoint functor theorem: if `C` is complete, well-powered and
has a small coseparating set, then it is cocomplete. -/
theorem hasColimits_of_hasLimits_of_isCoseparating [HasLimits C] [WellPowered C] {𝒢 : Set C}
@@ -142,7 +153,9 @@ theorem hasColimits_of_hasLimits_of_isCoseparating [HasLimits C] [WellPowered C]
has_colimits_of_shape_iff_is_right_adjoint_const.2
⟨is_right_adjoint_of_preserves_limits_of_is_coseparating h𝒢 _⟩ }
#align category_theory.limits.has_colimits_of_has_limits_of_is_coseparating CategoryTheory.Limits.hasColimits_of_hasLimits_of_isCoseparating
+-/
+#print CategoryTheory.Limits.hasLimits_of_hasColimits_of_isSeparating /-
/-- A consequence of the special adjoint functor theorem: if `C` is cocomplete, well-copowered and
has a small separating set, then it is complete. -/
theorem hasLimits_of_hasColimits_of_isSeparating [HasColimits C] [WellPowered Cᵒᵖ] {𝒢 : Set C}
@@ -152,6 +165,7 @@ theorem hasLimits_of_hasColimits_of_isSeparating [HasColimits C] [WellPowered C
has_limits_of_shape_iff_is_left_adjoint_const.2
⟨is_left_adjoint_of_preserves_colimits_of_is_separatig h𝒢 _⟩ }
#align category_theory.limits.has_limits_of_has_colimits_of_is_separating CategoryTheory.Limits.hasLimits_of_hasColimits_of_isSeparating
+-/
end Limits
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -80,7 +80,7 @@ if `G` satisfies the solution set condition then `G` is a right adjoint.
-/
noncomputable def isRightAdjointOfPreservesLimitsOfSolutionSetCondition [HasLimits D]
[PreservesLimits G] (hG : SolutionSetCondition G) : IsRightAdjoint G := by
- refine' @isRightAdjointOfStructuredArrowInitials _ _ _ _ G ?_
+ refine @isRightAdjointOfStructuredArrowInitials _ _ _ _ G ?_
intro A
specialize hG A
choose ι B f g using hG
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)
@@ -44,7 +44,6 @@ namespace CategoryTheory
open Limits
variable {J : Type v}
-
variable {C : Type u} [Category.{v} C]
/-- The functor `G : D ⥤ C` satisfies the *solution set condition* if for every `A : C`, there is a
@@ -64,7 +63,6 @@ def SolutionSetCondition {D : Type u} [Category.{v} D] (G : D ⥤ C) : Prop :=
section GeneralAdjointFunctorTheorem
variable {D : Type u} [Category.{v} D]
-
variable (G : D ⥤ C)
/-- If `G : D ⥤ C` is a right adjoint it satisfies the solution set condition. -/
@@ -2,11 +2,6 @@
Copyright (c) 2021 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.adjunction.adjoint_functor_theorems
-! leanprover-community/mathlib commit 361aa777b4d262212c31d7c4a245ccb23645c156
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Generator
import Mathlib.CategoryTheory.Limits.ConeCategory
@@ -14,6 +9,8 @@ import Mathlib.CategoryTheory.Limits.Constructions.WeaklyInitial
import Mathlib.CategoryTheory.Limits.FunctorCategory
import Mathlib.CategoryTheory.Subobject.Comma
+#align_import category_theory.adjunction.adjoint_functor_theorems from "leanprover-community/mathlib"@"361aa777b4d262212c31d7c4a245ccb23645c156"
+
/-!
# Adjoint functor theorem
@@ -60,8 +60,8 @@ adjoint functor theorem to go through.
-/
def SolutionSetCondition {D : Type u} [Category.{v} D] (G : D ⥤ C) : Prop :=
∀ A : C,
- ∃ (ι : Type v)(B : ι → D)(f : ∀ i : ι, A ⟶ G.obj (B i)),
- ∀ (X) (h : A ⟶ G.obj X), ∃ (i : ι)(g : B i ⟶ X), f i ≫ G.map g = h
+ ∃ (ι : Type v) (B : ι → D) (f : ∀ i : ι, A ⟶ G.obj (B i)),
+ ∀ (X) (h : A ⟶ G.obj X), ∃ (i : ι) (g : B i ⟶ X), f i ≫ G.map g = h
#align category_theory.solution_set_condition CategoryTheory.SolutionSetCondition
section GeneralAdjointFunctorTheorem
The unported dependencies are