category_theory.monad.equiv_monMathlib.CategoryTheory.Monad.EquivMon

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.

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -3,9 +3,9 @@ Copyright (c) 2020 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
-import Mathbin.CategoryTheory.Monad.Basic
-import Mathbin.CategoryTheory.Monoidal.End
-import Mathbin.CategoryTheory.Monoidal.Mon_
+import CategoryTheory.Monad.Basic
+import CategoryTheory.Monoidal.End
+import CategoryTheory.Monoidal.Mon_
 
 #align_import category_theory.monad.equiv_mon from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
 
Diff
@@ -2,16 +2,13 @@
 Copyright (c) 2020 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.monad.equiv_mon
-! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Monad.Basic
 import Mathbin.CategoryTheory.Monoidal.End
 import Mathbin.CategoryTheory.Monoidal.Mon_
 
+#align_import category_theory.monad.equiv_mon from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
+
 /-!
 
 # The equivalence between `Monad C` and `Mon_ (C ⥤ C)`.
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 
 ! This file was ported from Lean 3 source module category_theory.monad.equiv_mon
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.CategoryTheory.Monoidal.Mon_
 
 # The equivalence between `Monad C` and `Mon_ (C ⥤ C)`.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A monad "is just" a monoid in the category of endofunctors.
 
 # Definitions/Theorems
Diff
@@ -41,6 +41,7 @@ namespace Monad
 
 attribute [local instance, local reducible] endofunctor_monoidal_category
 
+#print CategoryTheory.Monad.toMon /-
 /-- To every `Monad C` we associated a monoid object in `C ⥤ C`.-/
 @[simps]
 def toMon : Monad C → Mon_ (C ⥤ C) := fun M =>
@@ -53,9 +54,11 @@ def toMon : Monad C → Mon_ (C ⥤ C) := fun M =>
     -- `obviously` provides this, but slowly
     mul_assoc' := by ext; dsimp; simp [M.assoc] }
 #align category_theory.Monad.to_Mon CategoryTheory.Monad.toMon
+-/
 
 variable (C)
 
+#print CategoryTheory.Monad.monadToMon /-
 /-- Passing from `Monad C` to `Mon_ (C ⥤ C)` is functorial. -/
 @[simps]
 def monadToMon : Monad C ⥤ Mon_ (C ⥤ C) where
@@ -65,9 +68,11 @@ def monadToMon : Monad C ⥤ Mon_ (C ⥤ C) where
   -- `obviously` provides this, but slowly
   map_comp' := by intro X Y Z f g; rfl
 #align category_theory.Monad.Monad_to_Mon CategoryTheory.Monad.monadToMon
+-/
 
 variable {C}
 
+#print CategoryTheory.Monad.ofMon /-
 /-- To every monoid object in `C ⥤ C` we associate a `Monad C`. -/
 @[simps]
 def ofMon : Mon_ (C ⥤ C) → Monad C := fun M =>
@@ -78,9 +83,11 @@ def ofMon : Mon_ (C ⥤ C) → Monad C := fun M =>
     right_unit' := fun X => by rw [← M.one.hcomp_id_app, ← nat_trans.comp_app, M.one_mul]; rfl
     assoc' := fun X => by rw [← nat_trans.hcomp_id_app, ← nat_trans.comp_app]; simp }
 #align category_theory.Monad.of_Mon CategoryTheory.Monad.ofMon
+-/
 
 variable (C)
 
+#print CategoryTheory.Monad.monToMonad /-
 /-- Passing from `Mon_ (C ⥤ C)` to `Monad C` is functorial. -/
 @[simps]
 def monToMonad : Mon_ (C ⥤ C) ⥤ Monad C where
@@ -98,6 +105,7 @@ def monToMonad : Mon_ (C ⥤ C) ⥤ Monad C where
         simpa only [nat_trans.naturality, nat_trans.hcomp_app, assoc, nat_trans.comp_app,
           of_Mon_μ] }
 #align category_theory.Monad.Mon_to_Monad CategoryTheory.Monad.monToMonad
+-/
 
 namespace MonadMonEquiv
 
@@ -112,17 +120,17 @@ def counitIso : monToMonad C ⋙ monadToMon C ≅ 𝟭 _
   hom_inv_id' := by ext; simp
   -- `obviously` provides these, but slowly
   inv_hom_id' := by ext; simp
-#align category_theory.Monad.Monad_Mon_equiv.counit_iso CategoryTheory.Monad.MonadMonEquiv.counitIso
+#align category_theory.Monad.Monad_Mon_equiv.counit_iso CategoryTheory.Monad.monadMonEquiv.counitIso
 
 /-- Auxiliary definition for `Monad_Mon_equiv` -/
 @[simps]
 def unitIsoHom : 𝟭 _ ⟶ monadToMon C ⋙ monToMonad C where app _ := { app := fun _ => 𝟙 _ }
-#align category_theory.Monad.Monad_Mon_equiv.unit_iso_hom CategoryTheory.Monad.MonadMonEquiv.unitIsoHom
+#align category_theory.Monad.Monad_Mon_equiv.unit_iso_hom CategoryTheory.Monad.monadMonEquiv.unitIsoHom
 
 /-- Auxiliary definition for `Monad_Mon_equiv` -/
 @[simps]
 def unitIsoInv : monadToMon C ⋙ monToMonad C ⟶ 𝟭 _ where app _ := { app := fun _ => 𝟙 _ }
-#align category_theory.Monad.Monad_Mon_equiv.unit_iso_inv CategoryTheory.Monad.MonadMonEquiv.unitIsoInv
+#align category_theory.Monad.Monad_Mon_equiv.unit_iso_inv CategoryTheory.Monad.monadMonEquiv.unitIsoInv
 
 /-- Isomorphism of functors used in `Monad_Mon_equiv` -/
 @[simps]
@@ -133,12 +141,13 @@ def unitIso : 𝟭 _ ≅ monadToMon C ⋙ monToMonad C
   hom_inv_id' := by ext; simp
   -- `obviously` provides these, but slowly
   inv_hom_id' := by ext; simp
-#align category_theory.Monad.Monad_Mon_equiv.unit_iso CategoryTheory.Monad.MonadMonEquiv.unitIso
+#align category_theory.Monad.Monad_Mon_equiv.unit_iso CategoryTheory.Monad.monadMonEquiv.unitIso
 
 end MonadMonEquiv
 
 open MonadMonEquiv
 
+#print CategoryTheory.Monad.monadMonEquiv /-
 /-- Oh, monads are just monoids in the category of endofunctors (equivalence of categories). -/
 @[simps]
 def monadMonEquiv : Monad C ≌ Mon_ (C ⥤ C)
@@ -149,6 +158,7 @@ def monadMonEquiv : Monad C ≌ Mon_ (C ⥤ C)
   counitIso := counitIso
   functor_unitIso_comp' := by intro X; ext; dsimp; simp
 #align category_theory.Monad.Monad_Mon_equiv CategoryTheory.Monad.monadMonEquiv
+-/
 
 -- `obviously`, slowly
 -- Sanity check
Diff
@@ -47,18 +47,11 @@ def toMon : Monad C → Mon_ (C ⥤ C) := fun M =>
   { pt := (M : C ⥤ C)
     one := M.η
     mul := M.μ
-    one_mul' := by
-      ext
-      simp
+    one_mul' := by ext; simp
     -- `obviously` provides this, but slowly
-    mul_one' := by
-      ext
-      simp
+    mul_one' := by ext; simp
     -- `obviously` provides this, but slowly
-    mul_assoc' := by
-      ext
-      dsimp
-      simp [M.assoc] }
+    mul_assoc' := by ext; dsimp; simp [M.assoc] }
 #align category_theory.Monad.to_Mon CategoryTheory.Monad.toMon
 
 variable (C)
@@ -68,13 +61,9 @@ variable (C)
 def monadToMon : Monad C ⥤ Mon_ (C ⥤ C) where
   obj := toMon
   map _ _ f := { Hom := f.toNatTrans }
-  map_id' := by
-    intro X
-    rfl
+  map_id' := by intro X; rfl
   -- `obviously` provides this, but slowly
-  map_comp' := by
-    intro X Y Z f g
-    rfl
+  map_comp' := by intro X Y Z f g; rfl
 #align category_theory.Monad.Monad_to_Mon CategoryTheory.Monad.monadToMon
 
 variable {C}
@@ -85,17 +74,9 @@ def ofMon : Mon_ (C ⥤ C) → Monad C := fun M =>
   { toFunctor := M.pt
     η' := M.one
     μ' := M.mul
-    left_unit' := fun X =>
-      by
-      rw [← M.one.id_hcomp_app, ← nat_trans.comp_app, M.mul_one]
-      rfl
-    right_unit' := fun X =>
-      by
-      rw [← M.one.hcomp_id_app, ← nat_trans.comp_app, M.one_mul]
-      rfl
-    assoc' := fun X => by
-      rw [← nat_trans.hcomp_id_app, ← nat_trans.comp_app]
-      simp }
+    left_unit' := fun X => by rw [← M.one.id_hcomp_app, ← nat_trans.comp_app, M.mul_one]; rfl
+    right_unit' := fun X => by rw [← M.one.hcomp_id_app, ← nat_trans.comp_app, M.one_mul]; rfl
+    assoc' := fun X => by rw [← nat_trans.hcomp_id_app, ← nat_trans.comp_app]; simp }
 #align category_theory.Monad.of_Mon CategoryTheory.Monad.ofMon
 
 variable (C)
@@ -128,13 +109,9 @@ def counitIso : monToMonad C ⋙ monadToMon C ≅ 𝟭 _
     where
   Hom := { app := fun _ => { Hom := 𝟙 _ } }
   inv := { app := fun _ => { Hom := 𝟙 _ } }
-  hom_inv_id' := by
-    ext
-    simp
+  hom_inv_id' := by ext; simp
   -- `obviously` provides these, but slowly
-  inv_hom_id' := by
-    ext
-    simp
+  inv_hom_id' := by ext; simp
 #align category_theory.Monad.Monad_Mon_equiv.counit_iso CategoryTheory.Monad.MonadMonEquiv.counitIso
 
 /-- Auxiliary definition for `Monad_Mon_equiv` -/
@@ -153,13 +130,9 @@ def unitIso : 𝟭 _ ≅ monadToMon C ⋙ monToMonad C
     where
   Hom := unitIsoHom
   inv := unitIsoInv
-  hom_inv_id' := by
-    ext
-    simp
+  hom_inv_id' := by ext; simp
   -- `obviously` provides these, but slowly
-  inv_hom_id' := by
-    ext
-    simp
+  inv_hom_id' := by ext; simp
 #align category_theory.Monad.Monad_Mon_equiv.unit_iso CategoryTheory.Monad.MonadMonEquiv.unitIso
 
 end MonadMonEquiv
@@ -174,11 +147,7 @@ def monadMonEquiv : Monad C ≌ Mon_ (C ⥤ C)
   inverse := monToMonad _
   unitIso := unitIso
   counitIso := counitIso
-  functor_unitIso_comp' := by
-    intro X
-    ext
-    dsimp
-    simp
+  functor_unitIso_comp' := by intro X; ext; dsimp; simp
 #align category_theory.Monad.Monad_Mon_equiv CategoryTheory.Monad.monadMonEquiv
 
 -- `obviously`, slowly
Diff
@@ -44,7 +44,7 @@ attribute [local instance, local reducible] endofunctor_monoidal_category
 /-- To every `Monad C` we associated a monoid object in `C ⥤ C`.-/
 @[simps]
 def toMon : Monad C → Mon_ (C ⥤ C) := fun M =>
-  { x := (M : C ⥤ C)
+  { pt := (M : C ⥤ C)
     one := M.η
     mul := M.μ
     one_mul' := by
@@ -82,7 +82,7 @@ variable {C}
 /-- To every monoid object in `C ⥤ C` we associate a `Monad C`. -/
 @[simps]
 def ofMon : Mon_ (C ⥤ C) → Monad C := fun M =>
-  { toFunctor := M.x
+  { toFunctor := M.pt
     η' := M.one
     μ' := M.mul
     left_unit' := fun X =>

Changes in mathlib4

mathlib3
mathlib4
style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

Diff
@@ -38,7 +38,7 @@ namespace Monad
 
 attribute [local instance] endofunctorMonoidalCategory
 
-/-- To every `Monad C` we associated a monoid object in `C ⥤ C`.-/
+/-- To every `Monad C` we associated a monoid object in `C ⥤ C`. -/
 @[simps]
 def toMon (M : Monad C) : Mon_ (C ⥤ C) where
   X := (M : C ⥤ C)
refactor(CategoryTheory/Monoidal/Braided): use monoidalComp in the proofs (#10078)
Diff
@@ -66,14 +66,14 @@ def ofMon (M : Mon_ (C ⥤ C)) : Monad C where
   μ' := M.mul
   left_unit' := fun X => by
     -- Porting note: now using `erw`
-    erw [← NatTrans.id_hcomp_app M.one, ← NatTrans.comp_app, M.mul_one]
+    erw [← whiskerLeft_app, ← NatTrans.comp_app, M.mul_one]
     rfl
   right_unit' := fun X => by
     -- Porting note: now using `erw`
-    erw [← NatTrans.hcomp_id_app M.one, ← NatTrans.comp_app, M.one_mul]
+    erw [← whiskerRight_app, ← NatTrans.comp_app, M.one_mul]
     rfl
   assoc' := fun X => by
-    rw [← NatTrans.hcomp_id_app, ← NatTrans.comp_app]
+    rw [← whiskerLeft_app, ← whiskerRight_app, ← NatTrans.comp_app]
     -- Porting note: had to add this step:
     erw [M.mul_assoc]
     simp
chore: move to v4.6.0-rc1, merging adaptations from bump/v4.6.0 (#10176)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

Diff
@@ -98,8 +98,8 @@ def monToMonad : Mon_ (C ⥤ C) ⥤ Monad C where
         intro Z
         erw [← NatTrans.comp_app, f.mul_hom]
         dsimp
-        simp only [NatTrans.naturality, NatTrans.hcomp_app, assoc, NatTrans.comp_app,
-          ofMon_μ] }
+        simp only [Category.assoc, NatTrans.naturality, ofMon_obj]
+        rfl }
 #align category_theory.Monad.Mon_to_Monad CategoryTheory.Monad.monToMonad
 
 /-- Oh, monads are just monoids in the category of endofunctors (equivalence of categories). -/
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 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.monad.equiv_mon
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Monad.Basic
 import Mathlib.CategoryTheory.Monoidal.End
 import Mathlib.CategoryTheory.Monoidal.Mon_
 
+#align_import category_theory.monad.equiv_mon from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 
 # The equivalence between `Monad C` and `Mon_ (C ⥤ C)`.
feat: port CategoryTheory.Monad.EquivMon (#5086)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

Dependencies 3 + 228

229 files ported (98.7%)
83641 lines ported (98.8%)
Show graph

The unported dependencies are