category_theory.monad.adjunction | Mathlib porting status

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

ea3009f6

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

86d1873c

bump to nightly-2024-04-29-08

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

6607d135

Diff

@@ -263,11 +263,11 @@ instance comparison_essSurj [Reflective R] :
 #align category_theory.reflective.comparison_ess_surj CategoryTheory.Reflective.comparison_essSurj
 -/
 
-#print CategoryTheory.Reflective.comparisonFull /-
-instance comparisonFull [CategoryTheory.Functor.Full R] [IsRightAdjoint R] :
+#print CategoryTheory.Reflective.comparison_full /-
+instance comparison_full [CategoryTheory.Functor.Full R] [IsRightAdjoint R] :
     CategoryTheory.Functor.Full (Monad.comparison (Adjunction.ofRightAdjoint R))
     where preimage X Y f := R.preimage f.f
-#align category_theory.reflective.comparison_full CategoryTheory.Reflective.comparisonFull
+#align category_theory.reflective.comparison_full CategoryTheory.Reflective.comparison_full
 -/
 
 end Reflective

86d1873c

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -128,13 +128,14 @@ theorem Monad.left_comparison (h : L ⊣ R) : L ⋙ Monad.comparison h = h.toMon
 #align category_theory.monad.left_comparison CategoryTheory.Monad.left_comparison
 -/
 
-instance [Faithful R] (h : L ⊣ R) : Faithful (Monad.comparison h)
+instance [CategoryTheory.Functor.Faithful R] (h : L ⊣ R) :
+    CategoryTheory.Functor.Faithful (Monad.comparison h)
     where map_injective' X Y f g w := R.map_injective (congr_arg Monad.Algebra.Hom.f w : _)
 
-instance (T : Monad C) : Full (Monad.comparison T.adj)
+instance (T : Monad C) : CategoryTheory.Functor.Full (Monad.comparison T.adj)
     where preimage X Y f := ⟨f.f, by simpa using f.h⟩
 
-instance (T : Monad C) : EssSurj (Monad.comparison T.adj)
+instance (T : Monad C) : CategoryTheory.Functor.EssSurj (Monad.comparison T.adj)
     where mem_essImage X :=
     ⟨{  A := X.A
         a := X.a
@@ -179,16 +180,16 @@ theorem Comonad.left_comparison (h : L ⊣ R) : R ⋙ Comonad.comparison h = h.t
 -/
 
 #print CategoryTheory.Comonad.comparison_faithful_of_faithful /-
-instance Comonad.comparison_faithful_of_faithful [Faithful L] (h : L ⊣ R) :
-    Faithful (Comonad.comparison h)
+instance Comonad.comparison_faithful_of_faithful [CategoryTheory.Functor.Faithful L] (h : L ⊣ R) :
+    CategoryTheory.Functor.Faithful (Comonad.comparison h)
     where map_injective' X Y f g w := L.map_injective (congr_arg Comonad.Coalgebra.Hom.f w : _)
 #align category_theory.comonad.comparison_faithful_of_faithful CategoryTheory.Comonad.comparison_faithful_of_faithful
 -/
 
-instance (G : Comonad C) : Full (Comonad.comparison G.adj)
+instance (G : Comonad C) : CategoryTheory.Functor.Full (Comonad.comparison G.adj)
     where preimage X Y f := ⟨f.f, by simpa using f.h⟩
 
-instance (G : Comonad C) : EssSurj (Comonad.comparison G.adj)
+instance (G : Comonad C) : CategoryTheory.Functor.EssSurj (Comonad.comparison G.adj)
     where mem_essImage X :=
     ⟨{  A := X.A
         a := X.a
@@ -200,7 +201,7 @@ instance (G : Comonad C) : EssSurj (Comonad.comparison G.adj)
 from `D` to the category of Eilenberg-Moore algebras for the adjunction is an equivalence.
 -/
 class MonadicRightAdjoint (R : D ⥤ C) extends IsRightAdjoint R where
-  eqv : IsEquivalence (Monad.comparison (Adjunction.ofRightAdjoint R))
+  eqv : CategoryTheory.Functor.IsEquivalence (Monad.comparison (Adjunction.ofRightAdjoint R))
 #align category_theory.monadic_right_adjoint CategoryTheory.MonadicRightAdjoint
 -/
 
@@ -210,15 +211,17 @@ A left adjoint functor `L : C ⥤ D` is *comonadic* if the comparison functor `c
 from `C` to the category of Eilenberg-Moore algebras for the adjunction is an equivalence.
 -/
 class ComonadicLeftAdjoint (L : C ⥤ D) extends IsLeftAdjoint L where
-  eqv : IsEquivalence (Comonad.comparison (Adjunction.ofLeftAdjoint L))
+  eqv : CategoryTheory.Functor.IsEquivalence (Comonad.comparison (Adjunction.ofLeftAdjoint L))
 #align category_theory.comonadic_left_adjoint CategoryTheory.ComonadicLeftAdjoint
 -/
 
 noncomputable instance (T : Monad C) : MonadicRightAdjoint T.forget :=
-  ⟨(Equivalence.ofFullyFaithfullyEssSurj _ : IsEquivalence (Monad.comparison T.adj))⟩
+  ⟨(CategoryTheory.Functor.IsEquivalence.ofFullyFaithfullyEssSurj _ :
+      CategoryTheory.Functor.IsEquivalence (Monad.comparison T.adj))⟩
 
 noncomputable instance (G : Comonad C) : ComonadicLeftAdjoint G.forget :=
-  ⟨(Equivalence.ofFullyFaithfullyEssSurj _ : IsEquivalence (Comonad.comparison G.adj))⟩
+  ⟨(CategoryTheory.Functor.IsEquivalence.ofFullyFaithfullyEssSurj _ :
+      CategoryTheory.Functor.IsEquivalence (Comonad.comparison G.adj))⟩
 
 #print CategoryTheory.μ_iso_of_reflective /-
 -- TODO: This holds more generally for idempotent adjunctions, not just reflective adjunctions.
@@ -246,7 +249,7 @@ instance [Reflective R] (X : (Adjunction.ofRightAdjoint R).toMonad.Algebra) :
 
 #print CategoryTheory.Reflective.comparison_essSurj /-
 instance comparison_essSurj [Reflective R] :
-    EssSurj (Monad.comparison (Adjunction.ofRightAdjoint R)) :=
+    CategoryTheory.Functor.EssSurj (Monad.comparison (Adjunction.ofRightAdjoint R)) :=
   by
   refine' ⟨fun X => ⟨(left_adjoint R).obj X.A, ⟨_⟩⟩⟩
   symm
@@ -261,8 +264,9 @@ instance comparison_essSurj [Reflective R] :
 -/
 
 #print CategoryTheory.Reflective.comparisonFull /-
-instance comparisonFull [Full R] [IsRightAdjoint R] :
-    Full (Monad.comparison (Adjunction.ofRightAdjoint R)) where preimage X Y f := R.preimage f.f
+instance comparisonFull [CategoryTheory.Functor.Full R] [IsRightAdjoint R] :
+    CategoryTheory.Functor.Full (Monad.comparison (Adjunction.ofRightAdjoint R))
+    where preimage X Y f := R.preimage f.f
 #align category_theory.reflective.comparison_full CategoryTheory.Reflective.comparisonFull
 -/
 
@@ -275,7 +279,7 @@ end Reflective
 /-- Any reflective inclusion has a monadic right adjoint.
     cf Prop 5.3.3 of [Riehl][riehl2017] -/
 noncomputable instance (priority := 100) monadicOfReflective [Reflective R] : MonadicRightAdjoint R
-    where eqv := Equivalence.ofFullyFaithfullyEssSurj _
+    where eqv := CategoryTheory.Functor.IsEquivalence.ofFullyFaithfullyEssSurj _
 #align category_theory.monadic_of_reflective CategoryTheory.monadicOfReflective
 -/

86d1873c

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2019 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.Adjunction.Reflective
-import Mathbin.CategoryTheory.Monad.Algebra
+import CategoryTheory.Adjunction.Reflective
+import CategoryTheory.Monad.Algebra
 
 #align_import category_theory.monad.adjunction from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"

86d1873c

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2019 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.monad.adjunction
-! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Adjunction.Reflective
 import Mathbin.CategoryTheory.Monad.Algebra
 
+#align_import category_theory.monad.adjunction from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
+
 /-!
 # Adjunctions and monads

86d1873c

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -74,19 +74,23 @@ def toComonad (h : L ⊣ R) : Comonad D
 #align category_theory.adjunction.to_comonad CategoryTheory.Adjunction.toComonad
 -/
 
+#print CategoryTheory.Adjunction.adjToMonadIso /-
 /-- The monad induced by the Eilenberg-Moore adjunction is the original monad.  -/
 @[simps]
 def adjToMonadIso (T : Monad C) : T.adj.toMonad ≅ T :=
   MonadIso.mk (NatIso.ofComponents (fun X => Iso.refl _) (by tidy)) (fun X => by dsimp; simp)
     fun X => by dsimp; simp
 #align category_theory.adjunction.adj_to_monad_iso CategoryTheory.Adjunction.adjToMonadIso
+-/
 
+#print CategoryTheory.Adjunction.adjToComonadIso /-
 /-- The comonad induced by the Eilenberg-Moore adjunction is the original comonad. -/
 @[simps]
 def adjToComonadIso (G : Comonad C) : G.adj.toComonad ≅ G :=
   ComonadIso.mk (NatIso.ofComponents (fun X => Iso.refl _) (by tidy)) (fun X => by dsimp; simp)
     fun X => by dsimp; simp
 #align category_theory.adjunction.adj_to_comonad_iso CategoryTheory.Adjunction.adjToComonadIso
+-/
 
 end Adjunction

86d1873c

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -74,12 +74,6 @@ def toComonad (h : L ⊣ R) : Comonad D
 #align category_theory.adjunction.to_comonad CategoryTheory.Adjunction.toComonad
 -/
 
-/- warning: category_theory.adjunction.adj_to_monad_iso -> CategoryTheory.Adjunction.adjToMonadIso is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (T : CategoryTheory.Monad.{u1, u2} C _inst_1), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Monad.{u1, u2} C _inst_1) (CategoryTheory.Monad.category.{u1, u2} C _inst_1) (CategoryTheory.Adjunction.toMonad.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.Monad.Algebra.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.Algebra.eilenbergMoore.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.free.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.forget.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.adj.{u1, u2} C _inst_1 T)) T
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (T : CategoryTheory.Monad.{u1, u2} C _inst_1), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Monad.{u1, u2} C _inst_1) (CategoryTheory.instCategoryMonad.{u1, u2} C _inst_1) (CategoryTheory.Adjunction.toMonad.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.Monad.Algebra.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.Algebra.eilenbergMoore.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.free.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.forget.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.adj.{u1, u2} C _inst_1 T)) T
-Case conversion may be inaccurate. Consider using '#align category_theory.adjunction.adj_to_monad_iso CategoryTheory.Adjunction.adjToMonadIsoₓ'. -/
 /-- The monad induced by the Eilenberg-Moore adjunction is the original monad.  -/
 @[simps]
 def adjToMonadIso (T : Monad C) : T.adj.toMonad ≅ T :=
@@ -87,12 +81,6 @@ def adjToMonadIso (T : Monad C) : T.adj.toMonad ≅ T :=
     fun X => by dsimp; simp
 #align category_theory.adjunction.adj_to_monad_iso CategoryTheory.Adjunction.adjToMonadIso
 
-/- warning: category_theory.adjunction.adj_to_comonad_iso -> CategoryTheory.Adjunction.adjToComonadIso is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (G : CategoryTheory.Comonad.{u1, u2} C _inst_1), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Comonad.{u1, u2} C _inst_1) (CategoryTheory.Comonad.category.{u1, u2} C _inst_1) (CategoryTheory.Adjunction.toComonad.{u1, u1, max u2 u1, u2} (CategoryTheory.Comonad.Coalgebra.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.Coalgebra.eilenbergMoore.{u1, u2} C _inst_1 G) C _inst_1 (CategoryTheory.Comonad.forget.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.cofree.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.adj.{u1, u2} C _inst_1 G)) G
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (G : CategoryTheory.Comonad.{u1, u2} C _inst_1), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Comonad.{u1, u2} C _inst_1) (CategoryTheory.instCategoryComonad.{u1, u2} C _inst_1) (CategoryTheory.Adjunction.toComonad.{u1, u1, max u2 u1, u2} (CategoryTheory.Comonad.Coalgebra.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.Coalgebra.eilenbergMoore.{u1, u2} C _inst_1 G) C _inst_1 (CategoryTheory.Comonad.forget.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.cofree.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.adj.{u1, u2} C _inst_1 G)) G
-Case conversion may be inaccurate. Consider using '#align category_theory.adjunction.adj_to_comonad_iso CategoryTheory.Adjunction.adjToComonadIsoₓ'. -/
 /-- The comonad induced by the Eilenberg-Moore adjunction is the original comonad. -/
 @[simps]
 def adjToComonadIso (G : Comonad C) : G.adj.toComonad ≅ G :=

86d1873c

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -54,14 +54,8 @@ def toMonad (h : L ⊣ R) : Monad C where
   toFunctor := L ⋙ R
   η' := h.Unit
   μ' := whiskerRight (whiskerLeft L h.counit) R
-  assoc' X := by
-    dsimp
-    rw [← R.map_comp]
-    simp
-  right_unit' X := by
-    dsimp
-    rw [← R.map_comp]
-    simp
+  assoc' X := by dsimp; rw [← R.map_comp]; simp
+  right_unit' X := by dsimp; rw [← R.map_comp]; simp
 #align category_theory.adjunction.to_monad CategoryTheory.Adjunction.toMonad
 -/
 
@@ -75,14 +69,8 @@ def toComonad (h : L ⊣ R) : Comonad D
   toFunctor := R ⋙ L
   ε' := h.counit
   δ' := whiskerRight (whiskerLeft R h.Unit) L
-  coassoc' X := by
-    dsimp
-    rw [← L.map_comp]
-    simp
-  right_counit' X := by
-    dsimp
-    rw [← L.map_comp]
-    simp
+  coassoc' X := by dsimp; rw [← L.map_comp]; simp
+  right_counit' X := by dsimp; rw [← L.map_comp]; simp
 #align category_theory.adjunction.to_comonad CategoryTheory.Adjunction.toComonad
 -/
 
@@ -95,13 +83,8 @@ Case conversion may be inaccurate. Consider using '#align category_theory.adjunc
 /-- The monad induced by the Eilenberg-Moore adjunction is the original monad.  -/
 @[simps]
 def adjToMonadIso (T : Monad C) : T.adj.toMonad ≅ T :=
-  MonadIso.mk (NatIso.ofComponents (fun X => Iso.refl _) (by tidy))
-    (fun X => by
-      dsimp
-      simp)
-    fun X => by
-    dsimp
-    simp
+  MonadIso.mk (NatIso.ofComponents (fun X => Iso.refl _) (by tidy)) (fun X => by dsimp; simp)
+    fun X => by dsimp; simp
 #align category_theory.adjunction.adj_to_monad_iso CategoryTheory.Adjunction.adjToMonadIso
 
 /- warning: category_theory.adjunction.adj_to_comonad_iso -> CategoryTheory.Adjunction.adjToComonadIso is a dubious translation:
@@ -113,13 +96,8 @@ Case conversion may be inaccurate. Consider using '#align category_theory.adjunc
 /-- The comonad induced by the Eilenberg-Moore adjunction is the original comonad. -/
 @[simps]
 def adjToComonadIso (G : Comonad C) : G.adj.toComonad ≅ G :=
-  ComonadIso.mk (NatIso.ofComponents (fun X => Iso.refl _) (by tidy))
-    (fun X => by
-      dsimp
-      simp)
-    fun X => by
-    dsimp
-    simp
+  ComonadIso.mk (NatIso.ofComponents (fun X => Iso.refl _) (by tidy)) (fun X => by dsimp; simp)
+    fun X => by dsimp; simp
 #align category_theory.adjunction.adj_to_comonad_iso CategoryTheory.Adjunction.adjToComonadIso
 
 end Adjunction
@@ -137,15 +115,10 @@ def Monad.comparison (h : L ⊣ R) : D ⥤ h.toMonad.Algebra
   obj X :=
     { A := R.obj X
       a := R.map (h.counit.app X)
-      assoc' := by
-        dsimp
-        rw [← R.map_comp, ← adjunction.counit_naturality, R.map_comp]
-        rfl }
+      assoc' := by dsimp; rw [← R.map_comp, ← adjunction.counit_naturality, R.map_comp]; rfl }
   map X Y f :=
     { f := R.map f
-      h' := by
-        dsimp
-        rw [← R.map_comp, adjunction.counit_naturality, R.map_comp] }
+      h' := by dsimp; rw [← R.map_comp, adjunction.counit_naturality, R.map_comp] }
 #align category_theory.monad.comparison CategoryTheory.Monad.comparison
 -/
 
@@ -191,16 +164,10 @@ def Comonad.comparison (h : L ⊣ R) : C ⥤ h.toComonad.Coalgebra
   obj X :=
     { A := L.obj X
       a := L.map (h.Unit.app X)
-      coassoc' := by
-        dsimp
-        rw [← L.map_comp, ← adjunction.unit_naturality, L.map_comp]
-        rfl }
+      coassoc' := by dsimp; rw [← L.map_comp, ← adjunction.unit_naturality, L.map_comp]; rfl }
   map X Y f :=
     { f := L.map f
-      h' := by
-        dsimp
-        rw [← L.map_comp]
-        simp }
+      h' := by dsimp; rw [← L.map_comp]; simp }
 #align category_theory.comonad.comparison CategoryTheory.Comonad.comparison
 -/
 
@@ -266,10 +233,8 @@ noncomputable instance (G : Comonad C) : ComonadicLeftAdjoint G.forget :=
 
 #print CategoryTheory.μ_iso_of_reflective /-
 -- TODO: This holds more generally for idempotent adjunctions, not just reflective adjunctions.
-instance μ_iso_of_reflective [Reflective R] : IsIso (Adjunction.ofRightAdjoint R).toMonad.μ :=
-  by
-  dsimp
-  infer_instance
+instance μ_iso_of_reflective [Reflective R] : IsIso (Adjunction.ofRightAdjoint R).toMonad.μ := by
+  dsimp; infer_instance
 #align category_theory.μ_iso_of_reflective CategoryTheory.μ_iso_of_reflective
 -/

86d1873c

bump to nightly-2023-04-22-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/52932b3a083d4142e78a15dc928084a22fea9ba0

21a90077

Diff

@@ -4,7 +4,7 @@ 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.monad.adjunction
-! leanprover-community/mathlib commit ea3009f6c1a37dc031f741382dbb3ed93c965620
+! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.Monad.Algebra
 /-!
 # Adjunctions and monads
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We develop the basic relationship between adjunctions and monads.
 
 Given an adjunction `h : L ⊣ R`, we have `h.to_monad : monad C` and `h.to_comonad : comonad D`.

ea3009f6

bump to nightly-2023-04-20-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

61a5184d

Diff

@@ -42,6 +42,7 @@ variable {L : C ⥤ D} {R : D ⥤ C}
 
 namespace Adjunction
 
+#print CategoryTheory.Adjunction.toMonad /-
 /-- For a pair of functors `L : C ⥤ D`, `R : D ⥤ C`, an adjunction `h : L ⊣ R` induces a monad on
 the category `C`.
 -/
@@ -59,7 +60,9 @@ def toMonad (h : L ⊣ R) : Monad C where
     rw [← R.map_comp]
     simp
 #align category_theory.adjunction.to_monad CategoryTheory.Adjunction.toMonad
+-/
 
+#print CategoryTheory.Adjunction.toComonad /-
 /-- For a pair of functors `L : C ⥤ D`, `R : D ⥤ C`, an adjunction `h : L ⊣ R` induces a comonad on
 the category `D`.
 -/
@@ -78,7 +81,14 @@ def toComonad (h : L ⊣ R) : Comonad D
     rw [← L.map_comp]
     simp
 #align category_theory.adjunction.to_comonad CategoryTheory.Adjunction.toComonad
+-/
 
+/- warning: category_theory.adjunction.adj_to_monad_iso -> CategoryTheory.Adjunction.adjToMonadIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (T : CategoryTheory.Monad.{u1, u2} C _inst_1), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Monad.{u1, u2} C _inst_1) (CategoryTheory.Monad.category.{u1, u2} C _inst_1) (CategoryTheory.Adjunction.toMonad.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.Monad.Algebra.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.Algebra.eilenbergMoore.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.free.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.forget.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.adj.{u1, u2} C _inst_1 T)) T
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (T : CategoryTheory.Monad.{u1, u2} C _inst_1), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Monad.{u1, u2} C _inst_1) (CategoryTheory.instCategoryMonad.{u1, u2} C _inst_1) (CategoryTheory.Adjunction.toMonad.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.Monad.Algebra.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.Algebra.eilenbergMoore.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.free.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.forget.{u1, u2} C _inst_1 T) (CategoryTheory.Monad.adj.{u1, u2} C _inst_1 T)) T
+Case conversion may be inaccurate. Consider using '#align category_theory.adjunction.adj_to_monad_iso CategoryTheory.Adjunction.adjToMonadIsoₓ'. -/
 /-- The monad induced by the Eilenberg-Moore adjunction is the original monad.  -/
 @[simps]
 def adjToMonadIso (T : Monad C) : T.adj.toMonad ≅ T :=
@@ -91,6 +101,12 @@ def adjToMonadIso (T : Monad C) : T.adj.toMonad ≅ T :=
     simp
 #align category_theory.adjunction.adj_to_monad_iso CategoryTheory.Adjunction.adjToMonadIso
 
+/- warning: category_theory.adjunction.adj_to_comonad_iso -> CategoryTheory.Adjunction.adjToComonadIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (G : CategoryTheory.Comonad.{u1, u2} C _inst_1), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Comonad.{u1, u2} C _inst_1) (CategoryTheory.Comonad.category.{u1, u2} C _inst_1) (CategoryTheory.Adjunction.toComonad.{u1, u1, max u2 u1, u2} (CategoryTheory.Comonad.Coalgebra.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.Coalgebra.eilenbergMoore.{u1, u2} C _inst_1 G) C _inst_1 (CategoryTheory.Comonad.forget.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.cofree.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.adj.{u1, u2} C _inst_1 G)) G
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (G : CategoryTheory.Comonad.{u1, u2} C _inst_1), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Comonad.{u1, u2} C _inst_1) (CategoryTheory.instCategoryComonad.{u1, u2} C _inst_1) (CategoryTheory.Adjunction.toComonad.{u1, u1, max u2 u1, u2} (CategoryTheory.Comonad.Coalgebra.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.Coalgebra.eilenbergMoore.{u1, u2} C _inst_1 G) C _inst_1 (CategoryTheory.Comonad.forget.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.cofree.{u1, u2} C _inst_1 G) (CategoryTheory.Comonad.adj.{u1, u2} C _inst_1 G)) G
+Case conversion may be inaccurate. Consider using '#align category_theory.adjunction.adj_to_comonad_iso CategoryTheory.Adjunction.adjToComonadIsoₓ'. -/
 /-- The comonad induced by the Eilenberg-Moore adjunction is the original comonad. -/
 @[simps]
 def adjToComonadIso (G : Comonad C) : G.adj.toComonad ≅ G :=
@@ -105,6 +121,7 @@ def adjToComonadIso (G : Comonad C) : G.adj.toComonad ≅ G :=
 
 end Adjunction
 
+#print CategoryTheory.Monad.comparison /-
 /-- Gven any adjunction `L ⊣ R`, there is a comparison functor `category_theory.monad.comparison R`
 sending objects `Y : D` to Eilenberg-Moore algebras for `L ⋙ R` with underlying object `R.obj X`.
 
@@ -127,7 +144,9 @@ def Monad.comparison (h : L ⊣ R) : D ⥤ h.toMonad.Algebra
         dsimp
         rw [← R.map_comp, adjunction.counit_naturality, R.map_comp] }
 #align category_theory.monad.comparison CategoryTheory.Monad.comparison
+-/
 
+#print CategoryTheory.Monad.comparisonForget /-
 /-- The underlying object of `(monad.comparison R).obj X` is just `R.obj X`.
 -/
 @[simps]
@@ -136,10 +155,13 @@ def Monad.comparisonForget (h : L ⊣ R) : Monad.comparison h ⋙ h.toMonad.forg
   Hom := { app := fun X => 𝟙 _ }
   inv := { app := fun X => 𝟙 _ }
 #align category_theory.monad.comparison_forget CategoryTheory.Monad.comparisonForget
+-/
 
+#print CategoryTheory.Monad.left_comparison /-
 theorem Monad.left_comparison (h : L ⊣ R) : L ⋙ Monad.comparison h = h.toMonad.free :=
   rfl
 #align category_theory.monad.left_comparison CategoryTheory.Monad.left_comparison
+-/
 
 instance [Faithful R] (h : L ⊣ R) : Faithful (Monad.comparison h)
     where map_injective' X Y f g w := R.map_injective (congr_arg Monad.Algebra.Hom.f w : _)
@@ -154,6 +176,7 @@ instance (T : Monad C) : EssSurj (Monad.comparison T.adj)
         unit' := by simpa using X.unit
         assoc' := by simpa using X.assoc }, ⟨Monad.Algebra.isoMk (Iso.refl _) (by simp)⟩⟩
 
+#print CategoryTheory.Comonad.comparison /-
 /--
 Gven any adjunction `L ⊣ R`, there is a comparison functor `category_theory.comonad.comparison L`
 sending objects `X : C` to Eilenberg-Moore coalgebras for `L ⋙ R` with underlying object
@@ -176,7 +199,9 @@ def Comonad.comparison (h : L ⊣ R) : C ⥤ h.toComonad.Coalgebra
         rw [← L.map_comp]
         simp }
 #align category_theory.comonad.comparison CategoryTheory.Comonad.comparison
+-/
 
+#print CategoryTheory.Comonad.comparisonForget /-
 /-- The underlying object of `(comonad.comparison L).obj X` is just `L.obj X`.
 -/
 @[simps]
@@ -186,15 +211,20 @@ def Comonad.comparisonForget {L : C ⥤ D} {R : D ⥤ C} (h : L ⊣ R) :
   Hom := { app := fun X => 𝟙 _ }
   inv := { app := fun X => 𝟙 _ }
 #align category_theory.comonad.comparison_forget CategoryTheory.Comonad.comparisonForget
+-/
 
+#print CategoryTheory.Comonad.left_comparison /-
 theorem Comonad.left_comparison (h : L ⊣ R) : R ⋙ Comonad.comparison h = h.toComonad.cofree :=
   rfl
 #align category_theory.comonad.left_comparison CategoryTheory.Comonad.left_comparison
+-/
 
+#print CategoryTheory.Comonad.comparison_faithful_of_faithful /-
 instance Comonad.comparison_faithful_of_faithful [Faithful L] (h : L ⊣ R) :
     Faithful (Comonad.comparison h)
     where map_injective' X Y f g w := L.map_injective (congr_arg Comonad.Coalgebra.Hom.f w : _)
 #align category_theory.comonad.comparison_faithful_of_faithful CategoryTheory.Comonad.comparison_faithful_of_faithful
+-/
 
 instance (G : Comonad C) : Full (Comonad.comparison G.adj)
     where preimage X Y f := ⟨f.f, by simpa using f.h⟩
@@ -206,13 +236,16 @@ instance (G : Comonad C) : EssSurj (Comonad.comparison G.adj)
         counit' := by simpa using X.counit
         coassoc' := by simpa using X.coassoc }, ⟨Comonad.Coalgebra.isoMk (Iso.refl _) (by simp)⟩⟩
 
+#print CategoryTheory.MonadicRightAdjoint /-
 /-- A right adjoint functor `R : D ⥤ C` is *monadic* if the comparison functor `monad.comparison R`
 from `D` to the category of Eilenberg-Moore algebras for the adjunction is an equivalence.
 -/
 class MonadicRightAdjoint (R : D ⥤ C) extends IsRightAdjoint R where
   eqv : IsEquivalence (Monad.comparison (Adjunction.ofRightAdjoint R))
 #align category_theory.monadic_right_adjoint CategoryTheory.MonadicRightAdjoint
+-/
 
+#print CategoryTheory.ComonadicLeftAdjoint /-
 /--
 A left adjoint functor `L : C ⥤ D` is *comonadic* if the comparison functor `comonad.comparison L`
 from `C` to the category of Eilenberg-Moore algebras for the adjunction is an equivalence.
@@ -220,6 +253,7 @@ from `C` to the category of Eilenberg-Moore algebras for the adjunction is an eq
 class ComonadicLeftAdjoint (L : C ⥤ D) extends IsLeftAdjoint L where
   eqv : IsEquivalence (Comonad.comparison (Adjunction.ofLeftAdjoint L))
 #align category_theory.comonadic_left_adjoint CategoryTheory.ComonadicLeftAdjoint
+-/
 
 noncomputable instance (T : Monad C) : MonadicRightAdjoint T.forget :=
   ⟨(Equivalence.ofFullyFaithfullyEssSurj _ : IsEquivalence (Monad.comparison T.adj))⟩
@@ -227,12 +261,14 @@ noncomputable instance (T : Monad C) : MonadicRightAdjoint T.forget :=
 noncomputable instance (G : Comonad C) : ComonadicLeftAdjoint G.forget :=
   ⟨(Equivalence.ofFullyFaithfullyEssSurj _ : IsEquivalence (Comonad.comparison G.adj))⟩
 
+#print CategoryTheory.μ_iso_of_reflective /-
 -- TODO: This holds more generally for idempotent adjunctions, not just reflective adjunctions.
 instance μ_iso_of_reflective [Reflective R] : IsIso (Adjunction.ofRightAdjoint R).toMonad.μ :=
   by
   dsimp
   infer_instance
 #align category_theory.μ_iso_of_reflective CategoryTheory.μ_iso_of_reflective
+-/
 
 attribute [instance] monadic_right_adjoint.eqv
 
@@ -251,6 +287,7 @@ instance [Reflective R] (X : (Adjunction.ofRightAdjoint R).toMonad.Algebra) :
         erw [X.unit]
         simp⟩⟩⟩
 
+#print CategoryTheory.Reflective.comparison_essSurj /-
 instance comparison_essSurj [Reflective R] :
     EssSurj (Monad.comparison (Adjunction.ofRightAdjoint R)) :=
   by
@@ -264,13 +301,17 @@ instance comparison_essSurj [Reflective R] :
     adjunction.right_triangle_components, comp_id]
   apply (X.unit_assoc _).symm
 #align category_theory.reflective.comparison_ess_surj CategoryTheory.Reflective.comparison_essSurj
+-/
 
+#print CategoryTheory.Reflective.comparisonFull /-
 instance comparisonFull [Full R] [IsRightAdjoint R] :
     Full (Monad.comparison (Adjunction.ofRightAdjoint R)) where preimage X Y f := R.preimage f.f
 #align category_theory.reflective.comparison_full CategoryTheory.Reflective.comparisonFull
+-/
 
 end Reflective
 
+#print CategoryTheory.monadicOfReflective /-
 -- It is possible to do this computably since the construction gives the data of the inverse, not
 -- just the existence of an inverse on each object.
 -- see Note [lower instance priority]
@@ -279,6 +320,7 @@ end Reflective
 noncomputable instance (priority := 100) monadicOfReflective [Reflective R] : MonadicRightAdjoint R
     where eqv := Equivalence.ofFullyFaithfullyEssSurj _
 #align category_theory.monadic_of_reflective CategoryTheory.monadicOfReflective
+-/
 
 end CategoryTheory

ea3009f6

bump to nightly-2023-04-20-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af

d6678ca6

Diff

@@ -115,7 +115,7 @@ and essentially surjective when `R` is reflective.
 def Monad.comparison (h : L ⊣ R) : D ⥤ h.toMonad.Algebra
     where
   obj X :=
-    { a := R.obj X
+    { A := R.obj X
       a := R.map (h.counit.app X)
       assoc' := by
         dsimp
@@ -149,7 +149,7 @@ instance (T : Monad C) : Full (Monad.comparison T.adj)
 
 instance (T : Monad C) : EssSurj (Monad.comparison T.adj)
     where mem_essImage X :=
-    ⟨{  a := X.a
+    ⟨{  A := X.A
         a := X.a
         unit' := by simpa using X.unit
         assoc' := by simpa using X.assoc }, ⟨Monad.Algebra.isoMk (Iso.refl _) (by simp)⟩⟩
@@ -163,7 +163,7 @@ sending objects `X : C` to Eilenberg-Moore coalgebras for `L ⋙ R` with underly
 def Comonad.comparison (h : L ⊣ R) : C ⥤ h.toComonad.Coalgebra
     where
   obj X :=
-    { a := L.obj X
+    { A := L.obj X
       a := L.map (h.Unit.app X)
       coassoc' := by
         dsimp
@@ -201,7 +201,7 @@ instance (G : Comonad C) : Full (Comonad.comparison G.adj)
 
 instance (G : Comonad C) : EssSurj (Comonad.comparison G.adj)
     where mem_essImage X :=
-    ⟨{  a := X.a
+    ⟨{  A := X.A
         a := X.a
         counit' := by simpa using X.counit
         coassoc' := by simpa using X.coassoc }, ⟨Comonad.Coalgebra.isoMk (Iso.refl _) (by simp)⟩⟩
@@ -241,7 +241,7 @@ attribute [instance] comonadic_left_adjoint.eqv
 namespace Reflective
 
 instance [Reflective R] (X : (Adjunction.ofRightAdjoint R).toMonad.Algebra) :
-    IsIso ((Adjunction.ofRightAdjoint R).Unit.app X.a) :=
+    IsIso ((Adjunction.ofRightAdjoint R).Unit.app X.A) :=
   ⟨⟨X.a,
       ⟨X.Unit, by
         dsimp only [functor.id_obj]
@@ -254,7 +254,7 @@ instance [Reflective R] (X : (Adjunction.ofRightAdjoint R).toMonad.Algebra) :
 instance comparison_essSurj [Reflective R] :
     EssSurj (Monad.comparison (Adjunction.ofRightAdjoint R)) :=
   by
-  refine' ⟨fun X => ⟨(left_adjoint R).obj X.a, ⟨_⟩⟩⟩
+  refine' ⟨fun X => ⟨(left_adjoint R).obj X.A, ⟨_⟩⟩⟩
   symm
   refine' monad.algebra.iso_mk _ _
   · exact as_iso ((adjunction.of_right_adjoint R).Unit.app X.A)

ea3009f6

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

ea3009f6

chore(CategoryTheory): make Functor.Full a Prop (#12449)

Before this PR, Functor.Full contained the data of the preimage of maps by a full functor F. This PR makes Functor.Full a proposition. This is to prevent any diamond to appear.

The lemma Functor.image_preimage is also renamed Functor.map_preimage.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

ce289a0e

Diff

@@ -127,7 +127,7 @@ instance [R.Faithful] (h : L ⊣ R) : (Monad.comparison h).Faithful where
   map_injective {_ _} _ _ w := R.map_injective (congr_arg Monad.Algebra.Hom.f w : _)
 
 instance (T : Monad C) : (Monad.comparison T.adj).Full where
-  preimage {_ _} f := ⟨f.f, by simpa using f.h⟩
+  map_surjective {_ _} f := ⟨⟨f.f, by simpa using f.h⟩, rfl⟩
 
 instance (T : Monad C) : (Monad.comparison T.adj).EssSurj where
   mem_essImage X :=
@@ -177,7 +177,7 @@ instance Comonad.comparison_faithful_of_faithful [L.Faithful] (h : L ⊣ R) :
 #align category_theory.comonad.comparison_faithful_of_faithful CategoryTheory.Comonad.comparison_faithful_of_faithful
 
 instance (G : Comonad C) : (Comonad.comparison G.adj).Full where
-  preimage f := ⟨f.f, by simpa using f.h⟩
+  map_surjective f := ⟨⟨f.f, by simpa using f.h⟩, rfl⟩
 
 instance (G : Comonad C) : (Comonad.comparison G.adj).EssSurj where
   mem_essImage X :=
@@ -245,10 +245,10 @@ instance comparison_essSurj [Reflective R] :
   apply (X.unit_assoc _).symm
 #align category_theory.reflective.comparison_ess_surj CategoryTheory.Reflective.comparison_essSurj
 
-instance comparisonFull [R.Full] [IsRightAdjoint R] :
+instance comparison_full [R.Full] [IsRightAdjoint R] :
     (Monad.comparison (Adjunction.ofRightAdjoint R)).Full where
-  preimage f := R.preimage f.f
-#align category_theory.reflective.comparison_full CategoryTheory.Reflective.comparisonFull
+  map_surjective f := ⟨R.preimage f.f, by aesop_cat⟩
+#align category_theory.reflective.comparison_full CategoryTheory.Reflective.comparison_full
 
 end Reflective

ea3009f6

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.

65b7affc

Diff

@@ -123,13 +123,13 @@ theorem Monad.left_comparison (h : L ⊣ R) : L ⋙ Monad.comparison h = h.toMon
   rfl
 #align category_theory.monad.left_comparison CategoryTheory.Monad.left_comparison
 
-instance [Faithful R] (h : L ⊣ R) : Faithful (Monad.comparison h) where
+instance [R.Faithful] (h : L ⊣ R) : (Monad.comparison h).Faithful where
   map_injective {_ _} _ _ w := R.map_injective (congr_arg Monad.Algebra.Hom.f w : _)
 
-instance (T : Monad C) : Full (Monad.comparison T.adj) where
+instance (T : Monad C) : (Monad.comparison T.adj).Full where
   preimage {_ _} f := ⟨f.f, by simpa using f.h⟩
 
-instance (T : Monad C) : EssSurj (Monad.comparison T.adj) where
+instance (T : Monad C) : (Monad.comparison T.adj).EssSurj where
   mem_essImage X :=
     ⟨{  A := X.A
         a := X.a
@@ -171,15 +171,15 @@ theorem Comonad.left_comparison (h : L ⊣ R) : R ⋙ Comonad.comparison h = h.t
   rfl
 #align category_theory.comonad.left_comparison CategoryTheory.Comonad.left_comparison
 
-instance Comonad.comparison_faithful_of_faithful [Faithful L] (h : L ⊣ R) :
-    Faithful (Comonad.comparison h) where
+instance Comonad.comparison_faithful_of_faithful [L.Faithful] (h : L ⊣ R) :
+    (Comonad.comparison h).Faithful where
   map_injective {_ _} _ _ w := L.map_injective (congr_arg Comonad.Coalgebra.Hom.f w : _)
 #align category_theory.comonad.comparison_faithful_of_faithful CategoryTheory.Comonad.comparison_faithful_of_faithful
 
-instance (G : Comonad C) : Full (Comonad.comparison G.adj) where
+instance (G : Comonad C) : (Comonad.comparison G.adj).Full where
   preimage f := ⟨f.f, by simpa using f.h⟩
 
-instance (G : Comonad C) : EssSurj (Comonad.comparison G.adj) where
+instance (G : Comonad C) : (Comonad.comparison G.adj).EssSurj where
   mem_essImage X :=
     ⟨{  A := X.A
         a := X.a
@@ -191,7 +191,7 @@ instance (G : Comonad C) : EssSurj (Comonad.comparison G.adj) where
 from `D` to the category of Eilenberg-Moore algebras for the adjunction is an equivalence.
 -/
 class MonadicRightAdjoint (R : D ⥤ C) extends IsRightAdjoint R where
-  eqv : IsEquivalence (Monad.comparison (Adjunction.ofRightAdjoint R))
+  eqv : (Monad.comparison (Adjunction.ofRightAdjoint R)).IsEquivalence
 #align category_theory.monadic_right_adjoint CategoryTheory.MonadicRightAdjoint
 
 /--
@@ -199,14 +199,14 @@ A left adjoint functor `L : C ⥤ D` is *comonadic* if the comparison functor `C
 from `C` to the category of Eilenberg-Moore algebras for the adjunction is an equivalence.
 -/
 class ComonadicLeftAdjoint (L : C ⥤ D) extends IsLeftAdjoint L where
-  eqv : IsEquivalence (Comonad.comparison (Adjunction.ofLeftAdjoint L))
+  eqv : (Comonad.comparison (Adjunction.ofLeftAdjoint L)).IsEquivalence
 #align category_theory.comonadic_left_adjoint CategoryTheory.ComonadicLeftAdjoint
 
 noncomputable instance (T : Monad C) : MonadicRightAdjoint T.forget :=
-  ⟨(Equivalence.ofFullyFaithfullyEssSurj _ : IsEquivalence (Monad.comparison T.adj))⟩
+  ⟨Functor.IsEquivalence.ofFullyFaithfullyEssSurj (Monad.comparison T.adj)⟩
 
 noncomputable instance (G : Comonad C) : ComonadicLeftAdjoint G.forget :=
-  ⟨(Equivalence.ofFullyFaithfullyEssSurj _ : IsEquivalence (Comonad.comparison G.adj))⟩
+  ⟨Functor.IsEquivalence.ofFullyFaithfullyEssSurj (Comonad.comparison G.adj)⟩
 
 -- TODO: This holds more generally for idempotent adjunctions, not just reflective adjunctions.
 instance μ_iso_of_reflective [Reflective R] : IsIso (Adjunction.ofRightAdjoint R).toMonad.μ := by
@@ -231,7 +231,7 @@ instance [Reflective R] (X : (Adjunction.ofRightAdjoint R).toMonad.Algebra) :
         simp⟩⟩⟩
 
 instance comparison_essSurj [Reflective R] :
-    EssSurj (Monad.comparison (Adjunction.ofRightAdjoint R)) := by
+    (Monad.comparison (Adjunction.ofRightAdjoint R)).EssSurj := by
   refine' ⟨fun X => ⟨(leftAdjoint R).obj X.A, ⟨_⟩⟩⟩
   symm
   refine' Monad.Algebra.isoMk _ _
@@ -245,8 +245,8 @@ instance comparison_essSurj [Reflective R] :
   apply (X.unit_assoc _).symm
 #align category_theory.reflective.comparison_ess_surj CategoryTheory.Reflective.comparison_essSurj
 
-instance comparisonFull [Full R] [IsRightAdjoint R] :
-    Full (Monad.comparison (Adjunction.ofRightAdjoint R)) where
+instance comparisonFull [R.Full] [IsRightAdjoint R] :
+    (Monad.comparison (Adjunction.ofRightAdjoint R)).Full where
   preimage f := R.preimage f.f
 #align category_theory.reflective.comparison_full CategoryTheory.Reflective.comparisonFull
 
@@ -259,7 +259,7 @@ end Reflective
     cf Prop 5.3.3 of [Riehl][riehl2017] -/
 noncomputable instance (priority := 100) monadicOfReflective [Reflective R] :
     MonadicRightAdjoint R where
-  eqv := Equivalence.ofFullyFaithfullyEssSurj _
+  eqv := Functor.IsEquivalence.ofFullyFaithfullyEssSurj _
 #align category_theory.monadic_of_reflective CategoryTheory.monadicOfReflective
 
 end CategoryTheory

ea3009f6

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)

75c86f04

Diff

@@ -34,7 +34,6 @@ universe v₁ v₂ u₁ u₂
 
 -- morphism levels before object levels. See note [category_theory universes].
 variable {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₂} D]
-
 variable {L : C ⥤ D} {R : D ⥤ C}
 
 namespace Adjunction

ea3009f6

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2019 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.monad.adjunction
-! leanprover-community/mathlib commit ea3009f6c1a37dc031f741382dbb3ed93c965620
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Adjunction.Reflective
 import Mathlib.CategoryTheory.Monad.Algebra
 
+#align_import category_theory.monad.adjunction from "leanprover-community/mathlib"@"ea3009f6c1a37dc031f741382dbb3ed93c965620"
+
 /-!
 # Adjunctions and monads

ea3009f6

chore: fix many typos (#4983)

These are all doc fixes

54b72114

Diff

@@ -94,7 +94,7 @@ def adjToComonadIso (G : Comonad C) : G.adj.toComonad ≅ G :=
 
 end Adjunction
 
-/-- Gven any adjunction `L ⊣ R`, there is a comparison functor `CategoryTheory.Monad.comparison R`
+/-- Given any adjunction `L ⊣ R`, there is a comparison functor `CategoryTheory.Monad.comparison R`
 sending objects `Y : D` to Eilenberg-Moore algebras for `L ⋙ R` with underlying object `R.obj X`.
 
 We later show that this is full when `R` is full, faithful when `R` is faithful,
@@ -142,7 +142,7 @@ instance (T : Monad C) : EssSurj (Monad.comparison T.adj) where
     ⟨Monad.Algebra.isoMk (Iso.refl _)⟩⟩
 
 /--
-Gven any adjunction `L ⊣ R`, there is a comparison functor `CategoryTheory.Comonad.comparison L`
+Given any adjunction `L ⊣ R`, there is a comparison functor `CategoryTheory.Comonad.comparison L`
 sending objects `X : C` to Eilenberg-Moore coalgebras for `L ⋙ R` with underlying object
 `L.obj X`.
 -/

ea3009f6

chore: review of automation in category theory (#4793)

Clean up of automation in the category theory library. Leaving out unnecessary proof steps, or fields done by aesop_cat, and making more use of available autoparameters.

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

5b958613

Diff

@@ -83,25 +83,13 @@ def toComonad (h : L ⊣ R) : Comonad D where
 /-- The monad induced by the Eilenberg-Moore adjunction is the original monad.  -/
 @[simps!]
 def adjToMonadIso (T : Monad C) : T.adj.toMonad ≅ T :=
-  MonadIso.mk (NatIso.ofComponents (fun X => Iso.refl _) (by aesop_cat))
-    (fun X => by
-      dsimp
-      simp)
-    fun X => by
-    dsimp
-    simp
+  MonadIso.mk (NatIso.ofComponents fun X => Iso.refl _)
 #align category_theory.adjunction.adj_to_monad_iso CategoryTheory.Adjunction.adjToMonadIso
 
 /-- The comonad induced by the Eilenberg-Moore adjunction is the original comonad. -/
 @[simps!]
 def adjToComonadIso (G : Comonad C) : G.adj.toComonad ≅ G :=
-  ComonadIso.mk (NatIso.ofComponents (fun X => Iso.refl _) (by aesop_cat))
-    (fun X => by
-      dsimp
-      simp)
-    fun X => by
-    dsimp
-    simp
+  ComonadIso.mk (NatIso.ofComponents fun X => Iso.refl _)
 #align category_theory.adjunction.adj_to_comonad_iso CategoryTheory.Adjunction.adjToComonadIso
 
 end Adjunction
@@ -139,18 +127,19 @@ theorem Monad.left_comparison (h : L ⊣ R) : L ⋙ Monad.comparison h = h.toMon
   rfl
 #align category_theory.monad.left_comparison CategoryTheory.Monad.left_comparison
 
-instance [Faithful R] (h : L ⊣ R) : Faithful (Monad.comparison h)
-    where map_injective {_ _} _ _ w := R.map_injective (congr_arg Monad.Algebra.Hom.f w : _)
+instance [Faithful R] (h : L ⊣ R) : Faithful (Monad.comparison h) where
+  map_injective {_ _} _ _ w := R.map_injective (congr_arg Monad.Algebra.Hom.f w : _)
 
-instance (T : Monad C) : Full (Monad.comparison T.adj)
-    where preimage {_ _} f := ⟨f.f, by simpa using f.h⟩
+instance (T : Monad C) : Full (Monad.comparison T.adj) where
+  preimage {_ _} f := ⟨f.f, by simpa using f.h⟩
 
-instance (T : Monad C) : EssSurj (Monad.comparison T.adj)
-    where mem_essImage X :=
+instance (T : Monad C) : EssSurj (Monad.comparison T.adj) where
+  mem_essImage X :=
     ⟨{  A := X.A
         a := X.a
         unit := by simpa using X.unit
-        assoc := by simpa using X.assoc }, ⟨Monad.Algebra.isoMk (Iso.refl _) (by simp)⟩⟩
+        assoc := by simpa using X.assoc },
+    ⟨Monad.Algebra.isoMk (Iso.refl _)⟩⟩
 
 /--
 Gven any adjunction `L ⊣ R`, there is a comparison functor `CategoryTheory.Comonad.comparison L`
@@ -187,19 +176,20 @@ theorem Comonad.left_comparison (h : L ⊣ R) : R ⋙ Comonad.comparison h = h.t
 #align category_theory.comonad.left_comparison CategoryTheory.Comonad.left_comparison
 
 instance Comonad.comparison_faithful_of_faithful [Faithful L] (h : L ⊣ R) :
-    Faithful (Comonad.comparison h)
-    where map_injective {_ _} _ _ w := L.map_injective (congr_arg Comonad.Coalgebra.Hom.f w : _)
+    Faithful (Comonad.comparison h) where
+  map_injective {_ _} _ _ w := L.map_injective (congr_arg Comonad.Coalgebra.Hom.f w : _)
 #align category_theory.comonad.comparison_faithful_of_faithful CategoryTheory.Comonad.comparison_faithful_of_faithful
 
-instance (G : Comonad C) : Full (Comonad.comparison G.adj)
-    where preimage f := ⟨f.f, by simpa using f.h⟩
+instance (G : Comonad C) : Full (Comonad.comparison G.adj) where
+  preimage f := ⟨f.f, by simpa using f.h⟩
 
-instance (G : Comonad C) : EssSurj (Comonad.comparison G.adj)
-    where mem_essImage X :=
+instance (G : Comonad C) : EssSurj (Comonad.comparison G.adj) where
+  mem_essImage X :=
     ⟨{  A := X.A
         a := X.a
         counit := by simpa using X.counit
-        coassoc := by simpa using X.coassoc }, ⟨Comonad.Coalgebra.isoMk (Iso.refl _) (by simp)⟩⟩
+        coassoc := by simpa using X.coassoc },
+      ⟨Comonad.Coalgebra.isoMk (Iso.refl _)⟩⟩
 
 /-- A right adjoint functor `R : D ⥤ C` is *monadic* if the comparison functor `Monad.comparison R`
 from `D` to the category of Eilenberg-Moore algebras for the adjunction is an equivalence.
@@ -229,7 +219,6 @@ instance μ_iso_of_reflective [Reflective R] : IsIso (Adjunction.ofRightAdjoint
 #align category_theory.μ_iso_of_reflective CategoryTheory.μ_iso_of_reflective
 
 attribute [instance] MonadicRightAdjoint.eqv
-
 attribute [instance] ComonadicLeftAdjoint.eqv
 
 namespace Reflective
@@ -261,7 +250,8 @@ instance comparison_essSurj [Reflective R] :
 #align category_theory.reflective.comparison_ess_surj CategoryTheory.Reflective.comparison_essSurj
 
 instance comparisonFull [Full R] [IsRightAdjoint R] :
-    Full (Monad.comparison (Adjunction.ofRightAdjoint R)) where preimage f := R.preimage f.f
+    Full (Monad.comparison (Adjunction.ofRightAdjoint R)) where
+  preimage f := R.preimage f.f
 #align category_theory.reflective.comparison_full CategoryTheory.Reflective.comparisonFull
 
 end Reflective
@@ -271,8 +261,9 @@ end Reflective
 -- see Note [lower instance priority]
 /-- Any reflective inclusion has a monadic right adjoint.
     cf Prop 5.3.3 of [Riehl][riehl2017] -/
-noncomputable instance (priority := 100) monadicOfReflective [Reflective R] : MonadicRightAdjoint R
-    where eqv := Equivalence.ofFullyFaithfullyEssSurj _
+noncomputable instance (priority := 100) monadicOfReflective [Reflective R] :
+    MonadicRightAdjoint R where
+  eqv := Equivalence.ofFullyFaithfullyEssSurj _
 #align category_theory.monadic_of_reflective CategoryTheory.monadicOfReflective
 
 end CategoryTheory

ea3009f6

feat: Port CategoryTheory.Monad.Adjunction (#3528)

~~This is still WIP.~~ There may be a change to reassoc that would make this nicer, see zulip

184ec5cb

`category_theory.monad.adjunction` ⟷ `Mathlib.CategoryTheory.Monad.Adjunction`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 91

category_theory.monad.adjunction ⟷ Mathlib.CategoryTheory.Monad.Adjunction

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 91

`category_theory.monad.adjunction` ⟷ `Mathlib.CategoryTheory.Monad.Adjunction`