category_theory.category.galois_connection
⟷
Mathlib.CategoryTheory.Category.GaloisConnection
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) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-/
-import Mathbin.CategoryTheory.Category.Preorder
-import Mathbin.CategoryTheory.Adjunction.Basic
-import Mathbin.Order.GaloisConnection
+import CategoryTheory.Category.Preorder
+import CategoryTheory.Adjunction.Basic
+import Order.GaloisConnection
#align_import category_theory.category.galois_connection from "leanprover-community/mathlib"@"3dadefa3f544b1db6214777fe47910739b54c66a"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-
-! This file was ported from Lean 3 source module category_theory.category.galois_connection
-! leanprover-community/mathlib commit 3dadefa3f544b1db6214777fe47910739b54c66a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Category.Preorder
import Mathbin.CategoryTheory.Adjunction.Basic
import Mathbin.Order.GaloisConnection
+#align_import category_theory.category.galois_connection from "leanprover-community/mathlib"@"3dadefa3f544b1db6214777fe47910739b54c66a"
+
/-!
# Galois connections between preorders are adjunctions.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -48,12 +48,14 @@ namespace CategoryTheory
variable {X : Type u} {Y : Type v} [Preorder X] [Preorder Y]
+#print CategoryTheory.Adjunction.gc /-
/-- An adjunction between preorder categories induces a galois connection.
-/
theorem Adjunction.gc {L : X ⥤ Y} {R : Y ⥤ X} (adj : L ⊣ R) : GaloisConnection L.obj R.obj :=
fun x y =>
⟨fun h => ((adj.homEquiv x y).toFun h.Hom).le, fun h => ((adj.homEquiv x y).invFun h.Hom).le⟩
#align category_theory.adjunction.gc CategoryTheory.Adjunction.gc
+-/
end CategoryTheory
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -48,12 +48,6 @@ namespace CategoryTheory
variable {X : Type u} {Y : Type v} [Preorder X] [Preorder Y]
-/- warning: category_theory.adjunction.gc -> CategoryTheory.Adjunction.gc is a dubious translation:
-lean 3 declaration is
- forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : Preorder.{u1} X] [_inst_2 : Preorder.{u2} Y] {L : CategoryTheory.Functor.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2)} {R : CategoryTheory.Functor.{u2, u1, u2, u1} Y (Preorder.smallCategory.{u2} Y _inst_2) X (Preorder.smallCategory.{u1} X _inst_1)}, (CategoryTheory.Adjunction.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2) L R) -> (GaloisConnection.{u1, u2} X Y _inst_1 _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2) L) (CategoryTheory.Functor.obj.{u2, u1, u2, u1} Y (Preorder.smallCategory.{u2} Y _inst_2) X (Preorder.smallCategory.{u1} X _inst_1) R))
-but is expected to have type
- forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : Preorder.{u1} X] [_inst_2 : Preorder.{u2} Y] {L : CategoryTheory.Functor.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2)} {R : CategoryTheory.Functor.{u2, u1, u2, u1} Y (Preorder.smallCategory.{u2} Y _inst_2) X (Preorder.smallCategory.{u1} X _inst_1)}, (CategoryTheory.Adjunction.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2) L R) -> (GaloisConnection.{u1, u2} X Y _inst_1 _inst_2 (Prefunctor.obj.{succ u1, succ u2, u1, u2} X (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} X (CategoryTheory.Category.toCategoryStruct.{u1, u1} X (Preorder.smallCategory.{u1} X _inst_1))) Y (CategoryTheory.CategoryStruct.toQuiver.{u2, u2} Y (CategoryTheory.Category.toCategoryStruct.{u2, u2} Y (Preorder.smallCategory.{u2} Y _inst_2))) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2) L)) (Prefunctor.obj.{succ u2, succ u1, u2, u1} Y (CategoryTheory.CategoryStruct.toQuiver.{u2, u2} Y (CategoryTheory.Category.toCategoryStruct.{u2, u2} Y (Preorder.smallCategory.{u2} Y _inst_2))) X (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} X (CategoryTheory.Category.toCategoryStruct.{u1, u1} X (Preorder.smallCategory.{u1} X _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u2, u1} Y (Preorder.smallCategory.{u2} Y _inst_2) X (Preorder.smallCategory.{u1} X _inst_1) R)))
-Case conversion may be inaccurate. Consider using '#align category_theory.adjunction.gc CategoryTheory.Adjunction.gcₓ'. -/
/-- An adjunction between preorder categories induces a galois connection.
-/
theorem Adjunction.gc {L : X ⥤ Y} {R : Y ⥤ X} (adj : L ⊣ R) : GaloisConnection L.obj R.obj :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
! This file was ported from Lean 3 source module category_theory.category.galois_connection
-! leanprover-community/mathlib commit d82b87871d9a274884dff5263fa4f5d93bcce1d6
+! leanprover-community/mathlib commit 3dadefa3f544b1db6214777fe47910739b54c66a
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -16,6 +16,9 @@ import Mathbin.Order.GaloisConnection
# Galois connections between preorders are adjunctions.
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
* `galois_connection.adjunction` is the adjunction associated to a galois connection.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -27,6 +27,7 @@ section
variable {X : Type u} {Y : Type v} [Preorder X] [Preorder Y]
+#print GaloisConnection.adjunction /-
/-- A galois connection between preorders induces an adjunction between the associated categories.
-/
def GaloisConnection.adjunction {l : X → Y} {u : Y → X} (gc : GaloisConnection l u) :
@@ -36,6 +37,7 @@ def GaloisConnection.adjunction {l : X → Y} {u : Y → X} (gc : GaloisConnecti
homEquiv := fun X Y =>
⟨fun f => (gc.le_u f.le).Hom, fun f => (gc.l_le f.le).Hom, by tidy, by tidy⟩ }
#align galois_connection.adjunction GaloisConnection.adjunction
+-/
end
@@ -43,6 +45,12 @@ namespace CategoryTheory
variable {X : Type u} {Y : Type v} [Preorder X] [Preorder Y]
+/- warning: category_theory.adjunction.gc -> CategoryTheory.Adjunction.gc is a dubious translation:
+lean 3 declaration is
+ forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : Preorder.{u1} X] [_inst_2 : Preorder.{u2} Y] {L : CategoryTheory.Functor.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2)} {R : CategoryTheory.Functor.{u2, u1, u2, u1} Y (Preorder.smallCategory.{u2} Y _inst_2) X (Preorder.smallCategory.{u1} X _inst_1)}, (CategoryTheory.Adjunction.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2) L R) -> (GaloisConnection.{u1, u2} X Y _inst_1 _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2) L) (CategoryTheory.Functor.obj.{u2, u1, u2, u1} Y (Preorder.smallCategory.{u2} Y _inst_2) X (Preorder.smallCategory.{u1} X _inst_1) R))
+but is expected to have type
+ forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : Preorder.{u1} X] [_inst_2 : Preorder.{u2} Y] {L : CategoryTheory.Functor.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2)} {R : CategoryTheory.Functor.{u2, u1, u2, u1} Y (Preorder.smallCategory.{u2} Y _inst_2) X (Preorder.smallCategory.{u1} X _inst_1)}, (CategoryTheory.Adjunction.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2) L R) -> (GaloisConnection.{u1, u2} X Y _inst_1 _inst_2 (Prefunctor.obj.{succ u1, succ u2, u1, u2} X (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} X (CategoryTheory.Category.toCategoryStruct.{u1, u1} X (Preorder.smallCategory.{u1} X _inst_1))) Y (CategoryTheory.CategoryStruct.toQuiver.{u2, u2} Y (CategoryTheory.Category.toCategoryStruct.{u2, u2} Y (Preorder.smallCategory.{u2} Y _inst_2))) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u2} X (Preorder.smallCategory.{u1} X _inst_1) Y (Preorder.smallCategory.{u2} Y _inst_2) L)) (Prefunctor.obj.{succ u2, succ u1, u2, u1} Y (CategoryTheory.CategoryStruct.toQuiver.{u2, u2} Y (CategoryTheory.Category.toCategoryStruct.{u2, u2} Y (Preorder.smallCategory.{u2} Y _inst_2))) X (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} X (CategoryTheory.Category.toCategoryStruct.{u1, u1} X (Preorder.smallCategory.{u1} X _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u2, u1} Y (Preorder.smallCategory.{u2} Y _inst_2) X (Preorder.smallCategory.{u1} X _inst_1) R)))
+Case conversion may be inaccurate. Consider using '#align category_theory.adjunction.gc CategoryTheory.Adjunction.gcₓ'. -/
/-- An adjunction between preorder categories induces a galois connection.
-/
theorem Adjunction.gc {L : X ⥤ Y} {R : Y ⥤ X} (adj : L ⊣ R) : GaloisConnection L.obj R.obj :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -2,16 +2,13 @@
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-
-! This file was ported from Lean 3 source module category_theory.category.galois_connection
-! leanprover-community/mathlib commit d82b87871d9a274884dff5263fa4f5d93bcce1d6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Category.Preorder
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.Order.GaloisConnection
+#align_import category_theory.category.galois_connection from "leanprover-community/mathlib"@"d82b87871d9a274884dff5263fa4f5d93bcce1d6"
+
/-!
# Galois connections between preorders are adjunctions.
All dependencies are ported!