algebra.homology.differential_object
⟷
Mathlib.Algebra.Homology.DifferentialObject
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/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -91,9 +91,9 @@ def dgoToHomologicalComplex :
{ pt := fun i => X.pt i
d := fun i j =>
if h : i + b = j then X.d i ≫ X.objEqToHom (show i + (1 : ℤ) • b = j by simp [h]) else 0
- shape' := fun i j w => by dsimp at w ; convert dif_neg w
+ shape' := fun i j w => by dsimp at w; convert dif_neg w
d_comp_d' := fun i j k hij hjk => by
- dsimp at hij hjk ; substs hij hjk
+ dsimp at hij hjk; substs hij hjk
have : X.d i ≫ X.d _ = _ := (congr_fun X.d_squared i : _)
reassoc! this
simp [this] }
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathbin.Algebra.Homology.HomologicalComplex
-import Mathbin.CategoryTheory.DifferentialObject
+import Algebra.Homology.HomologicalComplex
+import CategoryTheory.DifferentialObject
#align_import algebra.homology.differential_object from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebra.homology.differential_object
-! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.Homology.HomologicalComplex
import Mathbin.CategoryTheory.DifferentialObject
+#align_import algebra.homology.differential_object from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"
+
/-!
# Homological complexes are differential graded objects.
mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
! This file was ported from Lean 3 source module algebra.homology.differential_object
-! leanprover-community/mathlib commit b535c2d5d996acd9b0554b76395d9c920e186f4f
+! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
! 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.DifferentialObject
/-!
# Homological complexes are differential graded objects.
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
We verify that a `homological_complex` indexed by an `add_comm_group` is
essentially the same thing as a differential graded object.
mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9
@@ -36,38 +36,51 @@ variable {β : Type _} [AddCommGroup β] {b : β}
variable {V : Type _} [Category V] [HasZeroMorphisms V]
+#print CategoryTheory.DifferentialObject.objEqToHom /-
/-- Since `eq_to_hom` only preserves the fact that `X.X i = X.X j` but not `i = j`, this definition
is used to aid the simplifier. -/
-abbrev CategoryTheory.DifferentialObject.xEqToHom
+abbrev CategoryTheory.DifferentialObject.objEqToHom
(X : DifferentialObject (GradedObjectWithShift b V)) {i j : β} (h : i = j) : X.pt i ⟶ X.pt j :=
eqToHom (congr_arg X.pt h)
-#align category_theory.differential_object.X_eq_to_hom CategoryTheory.DifferentialObject.xEqToHom
+#align category_theory.differential_object.X_eq_to_hom CategoryTheory.DifferentialObject.objEqToHom
+-/
+#print CategoryTheory.DifferentialObject.objEqToHom_refl /-
@[simp]
-theorem CategoryTheory.DifferentialObject.xEqToHom_refl
- (X : DifferentialObject (GradedObjectWithShift b V)) (i : β) : X.xEqToHom (refl i) = 𝟙 _ :=
+theorem CategoryTheory.DifferentialObject.objEqToHom_refl
+ (X : DifferentialObject (GradedObjectWithShift b V)) (i : β) : X.objEqToHom (refl i) = 𝟙 _ :=
rfl
-#align category_theory.differential_object.X_eq_to_hom_refl CategoryTheory.DifferentialObject.xEqToHom_refl
+#align category_theory.differential_object.X_eq_to_hom_refl CategoryTheory.DifferentialObject.objEqToHom_refl
+-/
+#print CategoryTheory.DifferentialObject.objEqToHom_d /-
@[simp, reassoc]
-theorem eq_to_hom_d (X : DifferentialObject (GradedObjectWithShift b V)) {x y : β} (h : x = y) :
- X.xEqToHom h ≫ X.d y = X.d x ≫ X.xEqToHom (by cases h; rfl) := by cases h; dsimp; simp
-#align homological_complex.eq_to_hom_d HomologicalComplex.eq_to_hom_d
+theorem CategoryTheory.DifferentialObject.objEqToHom_d
+ (X : DifferentialObject (GradedObjectWithShift b V)) {x y : β} (h : x = y) :
+ X.objEqToHom h ≫ X.d y = X.d x ≫ X.objEqToHom (by cases h; rfl) := by cases h; dsimp; simp
+#align homological_complex.eq_to_hom_d CategoryTheory.DifferentialObject.objEqToHom_d
+-/
+#print HomologicalComplex.d_eqToHom /-
@[simp, reassoc]
theorem d_eqToHom (X : HomologicalComplex V (ComplexShape.up' b)) {x y z : β} (h : y = z) :
X.d x y ≫ eqToHom (congr_arg X.pt h) = X.d x z := by cases h; simp
#align homological_complex.d_eq_to_hom HomologicalComplex.d_eqToHom
+-/
+#print CategoryTheory.DifferentialObject.eqToHom_f' /-
@[simp, reassoc]
-theorem eq_to_hom_f' {X Y : DifferentialObject (GradedObjectWithShift b V)} (f : X ⟶ Y) {x y : β}
- (h : x = y) : X.xEqToHom h ≫ f.f y = f.f x ≫ Y.xEqToHom h := by cases h; simp
-#align homological_complex.eq_to_hom_f' HomologicalComplex.eq_to_hom_f'
+theorem CategoryTheory.DifferentialObject.eqToHom_f'
+ {X Y : DifferentialObject (GradedObjectWithShift b V)} (f : X ⟶ Y) {x y : β} (h : x = y) :
+ X.objEqToHom h ≫ f.f y = f.f x ≫ Y.objEqToHom h := by cases h; simp
+#align homological_complex.eq_to_hom_f' CategoryTheory.DifferentialObject.eqToHom_f'
+-/
variable (b V)
attribute [local reducible] graded_object.has_shift
+#print HomologicalComplex.dgoToHomologicalComplex /-
/-- The functor from differential graded objects to homological complexes.
-/
@[simps]
@@ -77,7 +90,7 @@ def dgoToHomologicalComplex :
obj X :=
{ pt := fun i => X.pt i
d := fun i j =>
- if h : i + b = j then X.d i ≫ X.xEqToHom (show i + (1 : ℤ) • b = j by simp [h]) else 0
+ if h : i + b = j then X.d i ≫ X.objEqToHom (show i + (1 : ℤ) • b = j by simp [h]) else 0
shape' := fun i j w => by dsimp at w ; convert dif_neg w
d_comp_d' := fun i j k hij hjk => by
dsimp at hij hjk ; substs hij hjk
@@ -94,11 +107,13 @@ def dgoToHomologicalComplex :
simp only [category.comp_id, eq_to_hom_refl, dif_pos rfl, this, category.assoc,
eq_to_hom_f'] }
#align homological_complex.dgo_to_homological_complex HomologicalComplex.dgoToHomologicalComplex
+-/
+#print HomologicalComplex.homologicalComplexToDGO /-
/-- The functor from homological complexes to differential graded objects.
-/
@[simps]
-def homologicalComplexToDgo :
+def homologicalComplexToDGO :
HomologicalComplex V (ComplexShape.up' b) ⥤ DifferentialObject (GradedObjectWithShift b V)
where
obj X :=
@@ -108,26 +123,30 @@ def homologicalComplexToDgo :
map X Y f :=
{ f := f.f
comm' := by ext i; dsimp; simp }
-#align homological_complex.homological_complex_to_dgo HomologicalComplex.homologicalComplexToDgo
+#align homological_complex.homological_complex_to_dgo HomologicalComplex.homologicalComplexToDGO
+-/
+#print HomologicalComplex.dgoEquivHomologicalComplexUnitIso /-
/-- The unit isomorphism for `dgo_equiv_homological_complex`.
-/
@[simps]
def dgoEquivHomologicalComplexUnitIso :
𝟭 (DifferentialObject (GradedObjectWithShift b V)) ≅
- dgoToHomologicalComplex b V ⋙ homologicalComplexToDgo b V :=
+ dgoToHomologicalComplex b V ⋙ homologicalComplexToDGO b V :=
NatIso.ofComponents
(fun X =>
{ Hom := { f := fun i => 𝟙 (X.pt i) }
inv := { f := fun i => 𝟙 (X.pt i) } })
(by tidy)
#align homological_complex.dgo_equiv_homological_complex_unit_iso HomologicalComplex.dgoEquivHomologicalComplexUnitIso
+-/
+#print HomologicalComplex.dgoEquivHomologicalComplexCounitIso /-
/-- The counit isomorphism for `dgo_equiv_homological_complex`.
-/
@[simps]
def dgoEquivHomologicalComplexCounitIso :
- homologicalComplexToDgo b V ⋙ dgoToHomologicalComplex b V ≅
+ homologicalComplexToDGO b V ⋙ dgoToHomologicalComplex b V ≅
𝟭 (HomologicalComplex V (ComplexShape.up' b)) :=
NatIso.ofComponents
(fun X =>
@@ -145,7 +164,9 @@ def dgoEquivHomologicalComplexCounitIso :
simp } })
(by tidy)
#align homological_complex.dgo_equiv_homological_complex_counit_iso HomologicalComplex.dgoEquivHomologicalComplexCounitIso
+-/
+#print HomologicalComplex.dgoEquivHomologicalComplex /-
/-- The category of differential graded objects in `V` is equivalent
to the category of homological complexes in `V`.
-/
@@ -154,10 +175,11 @@ def dgoEquivHomologicalComplex :
DifferentialObject (GradedObjectWithShift b V) ≌ HomologicalComplex V (ComplexShape.up' b)
where
Functor := dgoToHomologicalComplex b V
- inverse := homologicalComplexToDgo b V
+ inverse := homologicalComplexToDGO b V
unitIso := dgoEquivHomologicalComplexUnitIso b V
counitIso := dgoEquivHomologicalComplexCounitIso b V
#align homological_complex.dgo_equiv_homological_complex HomologicalComplex.dgoEquivHomologicalComplex
+-/
end HomologicalComplex
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -78,16 +78,16 @@ def dgoToHomologicalComplex :
{ pt := fun i => X.pt i
d := fun i j =>
if h : i + b = j then X.d i ≫ X.xEqToHom (show i + (1 : ℤ) • b = j by simp [h]) else 0
- shape' := fun i j w => by dsimp at w; convert dif_neg w
+ shape' := fun i j w => by dsimp at w ; convert dif_neg w
d_comp_d' := fun i j k hij hjk => by
- dsimp at hij hjk; substs hij hjk
+ dsimp at hij hjk ; substs hij hjk
have : X.d i ≫ X.d _ = _ := (congr_fun X.d_squared i : _)
reassoc! this
simp [this] }
map X Y f :=
{ f := f.f
comm' := fun i j h => by
- dsimp at h⊢
+ dsimp at h ⊢
subst h
have : f.f i ≫ Y.d i = X.d i ≫ f.f (i + 1 • b) := (congr_fun f.comm i).symm
reassoc! this
@@ -134,13 +134,13 @@ def dgoEquivHomologicalComplexCounitIso :
{ Hom :=
{ f := fun i => 𝟙 (X.pt i)
comm' := fun i j h => by
- dsimp at h⊢; subst h
+ dsimp at h ⊢; subst h
delta homological_complex_to_dgo
simp }
inv :=
{ f := fun i => 𝟙 (X.pt i)
comm' := fun i j h => by
- dsimp at h⊢; subst h
+ dsimp at h ⊢; subst h
delta homological_complex_to_dgo
simp } })
(by tidy)
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -26,7 +26,7 @@ open CategoryTheory
open CategoryTheory.Limits
-open Classical
+open scoped Classical
noncomputable section
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -51,32 +51,17 @@ theorem CategoryTheory.DifferentialObject.xEqToHom_refl
@[simp, reassoc]
theorem eq_to_hom_d (X : DifferentialObject (GradedObjectWithShift b V)) {x y : β} (h : x = y) :
- X.xEqToHom h ≫ X.d y =
- X.d x ≫
- X.xEqToHom
- (by
- cases h
- rfl) :=
- by
- cases h
- dsimp
- simp
+ X.xEqToHom h ≫ X.d y = X.d x ≫ X.xEqToHom (by cases h; rfl) := by cases h; dsimp; simp
#align homological_complex.eq_to_hom_d HomologicalComplex.eq_to_hom_d
@[simp, reassoc]
theorem d_eqToHom (X : HomologicalComplex V (ComplexShape.up' b)) {x y z : β} (h : y = z) :
- X.d x y ≫ eqToHom (congr_arg X.pt h) = X.d x z :=
- by
- cases h
- simp
+ X.d x y ≫ eqToHom (congr_arg X.pt h) = X.d x z := by cases h; simp
#align homological_complex.d_eq_to_hom HomologicalComplex.d_eqToHom
@[simp, reassoc]
theorem eq_to_hom_f' {X Y : DifferentialObject (GradedObjectWithShift b V)} (f : X ⟶ Y) {x y : β}
- (h : x = y) : X.xEqToHom h ≫ f.f y = f.f x ≫ Y.xEqToHom h :=
- by
- cases h
- simp
+ (h : x = y) : X.xEqToHom h ≫ f.f y = f.f x ≫ Y.xEqToHom h := by cases h; simp
#align homological_complex.eq_to_hom_f' HomologicalComplex.eq_to_hom_f'
variable (b V)
@@ -93,9 +78,7 @@ def dgoToHomologicalComplex :
{ pt := fun i => X.pt i
d := fun i j =>
if h : i + b = j then X.d i ≫ X.xEqToHom (show i + (1 : ℤ) • b = j by simp [h]) else 0
- shape' := fun i j w => by
- dsimp at w
- convert dif_neg w
+ shape' := fun i j w => by dsimp at w; convert dif_neg w
d_comp_d' := fun i j k hij hjk => by
dsimp at hij hjk; substs hij hjk
have : X.d i ≫ X.d _ = _ := (congr_fun X.d_squared i : _)
@@ -121,16 +104,10 @@ def homologicalComplexToDgo :
obj X :=
{ pt := fun i => X.pt i
d := fun i => X.d i (i + 1 • b)
- d_squared' := by
- ext i
- dsimp
- simp }
+ d_squared' := by ext i; dsimp; simp }
map X Y f :=
{ f := f.f
- comm' := by
- ext i
- dsimp
- simp }
+ comm' := by ext i; dsimp; simp }
#align homological_complex.homological_complex_to_dgo HomologicalComplex.homologicalComplexToDgo
/-- The unit isomorphism for `dgo_equiv_homological_complex`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -49,7 +49,7 @@ theorem CategoryTheory.DifferentialObject.xEqToHom_refl
rfl
#align category_theory.differential_object.X_eq_to_hom_refl CategoryTheory.DifferentialObject.xEqToHom_refl
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem eq_to_hom_d (X : DifferentialObject (GradedObjectWithShift b V)) {x y : β} (h : x = y) :
X.xEqToHom h ≫ X.d y =
X.d x ≫
@@ -63,7 +63,7 @@ theorem eq_to_hom_d (X : DifferentialObject (GradedObjectWithShift b V)) {x y :
simp
#align homological_complex.eq_to_hom_d HomologicalComplex.eq_to_hom_d
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem d_eqToHom (X : HomologicalComplex V (ComplexShape.up' b)) {x y z : β} (h : y = z) :
X.d x y ≫ eqToHom (congr_arg X.pt h) = X.d x z :=
by
@@ -71,7 +71,7 @@ theorem d_eqToHom (X : HomologicalComplex V (ComplexShape.up' b)) {x y z : β} (
simp
#align homological_complex.d_eq_to_hom HomologicalComplex.d_eqToHom
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem eq_to_hom_f' {X Y : DifferentialObject (GradedObjectWithShift b V)} (f : X ⟶ Y) {x y : β}
(h : x = y) : X.xEqToHom h ≫ f.f y = f.f x ≫ Y.xEqToHom h :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -39,8 +39,8 @@ variable {V : Type _} [Category V] [HasZeroMorphisms V]
/-- Since `eq_to_hom` only preserves the fact that `X.X i = X.X j` but not `i = j`, this definition
is used to aid the simplifier. -/
abbrev CategoryTheory.DifferentialObject.xEqToHom
- (X : DifferentialObject (GradedObjectWithShift b V)) {i j : β} (h : i = j) : X.x i ⟶ X.x j :=
- eqToHom (congr_arg X.x h)
+ (X : DifferentialObject (GradedObjectWithShift b V)) {i j : β} (h : i = j) : X.pt i ⟶ X.pt j :=
+ eqToHom (congr_arg X.pt h)
#align category_theory.differential_object.X_eq_to_hom CategoryTheory.DifferentialObject.xEqToHom
@[simp]
@@ -65,7 +65,7 @@ theorem eq_to_hom_d (X : DifferentialObject (GradedObjectWithShift b V)) {x y :
@[simp, reassoc.1]
theorem d_eqToHom (X : HomologicalComplex V (ComplexShape.up' b)) {x y z : β} (h : y = z) :
- X.d x y ≫ eqToHom (congr_arg X.x h) = X.d x z :=
+ X.d x y ≫ eqToHom (congr_arg X.pt h) = X.d x z :=
by
cases h
simp
@@ -90,7 +90,7 @@ def dgoToHomologicalComplex :
DifferentialObject (GradedObjectWithShift b V) ⥤ HomologicalComplex V (ComplexShape.up' b)
where
obj X :=
- { x := fun i => X.x i
+ { pt := fun i => X.pt i
d := fun i j =>
if h : i + b = j then X.d i ≫ X.xEqToHom (show i + (1 : ℤ) • b = j by simp [h]) else 0
shape' := fun i j w => by
@@ -119,7 +119,7 @@ def homologicalComplexToDgo :
HomologicalComplex V (ComplexShape.up' b) ⥤ DifferentialObject (GradedObjectWithShift b V)
where
obj X :=
- { x := fun i => X.x i
+ { pt := fun i => X.pt i
d := fun i => X.d i (i + 1 • b)
d_squared' := by
ext i
@@ -141,8 +141,8 @@ def dgoEquivHomologicalComplexUnitIso :
dgoToHomologicalComplex b V ⋙ homologicalComplexToDgo b V :=
NatIso.ofComponents
(fun X =>
- { Hom := { f := fun i => 𝟙 (X.x i) }
- inv := { f := fun i => 𝟙 (X.x i) } })
+ { Hom := { f := fun i => 𝟙 (X.pt i) }
+ inv := { f := fun i => 𝟙 (X.pt i) } })
(by tidy)
#align homological_complex.dgo_equiv_homological_complex_unit_iso HomologicalComplex.dgoEquivHomologicalComplexUnitIso
@@ -155,13 +155,13 @@ def dgoEquivHomologicalComplexCounitIso :
NatIso.ofComponents
(fun X =>
{ Hom :=
- { f := fun i => 𝟙 (X.x i)
+ { f := fun i => 𝟙 (X.pt i)
comm' := fun i j h => by
dsimp at h⊢; subst h
delta homological_complex_to_dgo
simp }
inv :=
- { f := fun i => 𝟙 (X.x i)
+ { f := fun i => 𝟙 (X.pt i)
comm' := fun i j h => by
dsimp at h⊢; subst h
delta homological_complex_to_dgo
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
... or reduce its scope (the full removal is not as obvious).
@@ -18,9 +18,6 @@ This equivalence is probably not particularly useful in practice;
it's here to check that definitions match up as expected.
-/
-set_option autoImplicit true
-
-
open CategoryTheory CategoryTheory.Limits
open scoped Classical
@@ -58,7 +55,7 @@ theorem objEqToHom_d {x y : β} (h : x = y) :
#align homological_complex.eq_to_hom_d CategoryTheory.DifferentialObject.objEqToHom_d
@[reassoc (attr := simp)]
-theorem d_squared_apply : X.d x ≫ X.d _ = 0 := congr_fun X.d_squared _
+theorem d_squared_apply {x : β} : X.d x ≫ X.d _ = 0 := congr_fun X.d_squared _
@[reassoc (attr := simp)]
theorem eqToHom_f' {X Y : DifferentialObject ℤ (GradedObjectWithShift b V)} (f : X ⟶ Y) {x y : β}
@@ -82,7 +82,7 @@ theorem d_eqToHom (X : HomologicalComplex V (ComplexShape.up' b)) {x y z : β} (
X.d x y ≫ eqToHom (congr_arg X.X h) = X.d x z := by cases h; simp
#align homological_complex.d_eq_to_hom HomologicalComplex.d_eqToHom
-set_option maxHeartbeats 800000 in
+set_option maxHeartbeats 400000 in
/-- The functor from differential graded objects to homological complexes.
-/
@[simps]
Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.
The intent of this PR is to make autoImplicit
opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true
in the few files that rely on it.
That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.
I claim that many of the uses of autoImplicit
in these files are accidental; situations such as:
variables
are in scope, but pasting the lemma in the wrong sectionHaving set_option autoImplicit false
as the default prevents these types of mistake being made in the 90% of files where autoImplicit
s are not used at all, and causes them to be caught by CI during review.
I think there were various points during the port where we encouraged porters to delete the universes u v
lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.
A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18
as the no:dontcare:yes
vote ratio.
While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true
has been placed locally within a section, rather than at the top of the file.
@@ -18,6 +18,8 @@ This equivalence is probably not particularly useful in practice;
it's here to check that definitions match up as expected.
-/
+set_option autoImplicit true
+
open CategoryTheory CategoryTheory.Limits
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -32,8 +32,8 @@ Porting note: after the port, move these to their own file.
-/
namespace CategoryTheory.DifferentialObject
-variable {β : Type _} [AddCommGroup β] {b : β}
-variable {V : Type _} [Category V] [HasZeroMorphisms V]
+variable {β : Type*} [AddCommGroup β] {b : β}
+variable {V : Type*} [Category V] [HasZeroMorphisms V]
variable (X : DifferentialObject ℤ (GradedObjectWithShift b V))
/-- Since `eqToHom` only preserves the fact that `X.X i = X.X j` but not `i = j`, this definition
@@ -69,8 +69,8 @@ open CategoryTheory.DifferentialObject
namespace HomologicalComplex
-variable {β : Type _} [AddCommGroup β] (b : β)
-variable (V : Type _) [Category V] [HasZeroMorphisms V]
+variable {β : Type*} [AddCommGroup β] (b : β)
+variable (V : Type*) [Category V] [HasZeroMorphisms V]
-- Porting note: this should be moved to an earlier file.
-- Porting note: simpNF linter silenced, both `d_eqToHom` and its `_assoc` version
@@ -100,8 +100,7 @@ def dgoToHomologicalComplex :
comm' := fun i j h => by
dsimp at h ⊢
subst h
- simp [Category.comp_id, eqToHom_refl, dif_pos rfl, Category.assoc,
- eqToHom_f']
+ simp only [dite_true, Category.assoc, eqToHom_f']
-- Porting note: this `rw` used to be part of the `simp`.
have : f.f i ≫ Y.d i = X.d i ≫ f.f _ := (congr_fun f.comm i).symm
rw [reassoc_of% this] }
@@ -146,7 +145,7 @@ to the category of homological complexes in `V`.
-/
@[simps]
def dgoEquivHomologicalComplex :
- DifferentialObject ℤ (GradedObjectWithShift b V) ≌
+ DifferentialObject ℤ (GradedObjectWithShift b V) ≌
HomologicalComplex V (ComplexShape.up' b) where
functor := dgoToHomologicalComplex b V
inverse := homologicalComplexToDGO b V
What I was really hoping to do was show that ℕ-graded DGOs were the same as ℕ-graded chain complexes (we have the ℤ version), but this still seems awkward. If anyone would like to help with that, please let me know. I think this might be helpful in constructor tensor products of chain complexes with less suffering.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -34,7 +34,7 @@ namespace CategoryTheory.DifferentialObject
variable {β : Type _} [AddCommGroup β] {b : β}
variable {V : Type _} [Category V] [HasZeroMorphisms V]
-variable (X : DifferentialObject (GradedObjectWithShift b V))
+variable (X : DifferentialObject ℤ (GradedObjectWithShift b V))
/-- Since `eqToHom` only preserves the fact that `X.X i = X.X j` but not `i = j`, this definition
is used to aid the simplifier. -/
@@ -59,7 +59,7 @@ theorem objEqToHom_d {x y : β} (h : x = y) :
theorem d_squared_apply : X.d x ≫ X.d _ = 0 := congr_fun X.d_squared _
@[reassoc (attr := simp)]
-theorem eqToHom_f' {X Y : DifferentialObject (GradedObjectWithShift b V)} (f : X ⟶ Y) {x y : β}
+theorem eqToHom_f' {X Y : DifferentialObject ℤ (GradedObjectWithShift b V)} (f : X ⟶ Y) {x y : β}
(h : x = y) : X.objEqToHom h ≫ f.f y = f.f x ≫ Y.objEqToHom h := by cases h; simp
#align homological_complex.eq_to_hom_f' CategoryTheory.DifferentialObject.eqToHom_f'
@@ -85,7 +85,7 @@ set_option maxHeartbeats 800000 in
-/
@[simps]
def dgoToHomologicalComplex :
- DifferentialObject (GradedObjectWithShift b V) ⥤
+ DifferentialObject ℤ (GradedObjectWithShift b V) ⥤
HomologicalComplex V (ComplexShape.up' b) where
obj X :=
{ X := fun i => X.obj i
@@ -112,7 +112,7 @@ def dgoToHomologicalComplex :
@[simps]
def homologicalComplexToDGO :
HomologicalComplex V (ComplexShape.up' b) ⥤
- DifferentialObject (GradedObjectWithShift b V) where
+ DifferentialObject ℤ (GradedObjectWithShift b V) where
obj X :=
{ obj := fun i => X.X i
d := fun i => X.d i _ }
@@ -123,7 +123,7 @@ def homologicalComplexToDGO :
-/
@[simps!]
def dgoEquivHomologicalComplexUnitIso :
- 𝟭 (DifferentialObject (GradedObjectWithShift b V)) ≅
+ 𝟭 (DifferentialObject ℤ (GradedObjectWithShift b V)) ≅
dgoToHomologicalComplex b V ⋙ homologicalComplexToDGO b V :=
NatIso.ofComponents (fun X =>
{ hom := { f := fun i => 𝟙 (X.obj i) }
@@ -146,7 +146,8 @@ to the category of homological complexes in `V`.
-/
@[simps]
def dgoEquivHomologicalComplex :
- DifferentialObject (GradedObjectWithShift b V) ≌ HomologicalComplex V (ComplexShape.up' b) where
+ DifferentialObject ℤ (GradedObjectWithShift b V) ≌
+ HomologicalComplex V (ComplexShape.up' b) where
functor := dgoToHomologicalComplex b V
inverse := homologicalComplexToDGO b V
unitIso := dgoEquivHomologicalComplexUnitIso b V
@@ -2,15 +2,12 @@
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebra.homology.differential_object
-! leanprover-community/mathlib commit b535c2d5d996acd9b0554b76395d9c920e186f4f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.Homology.HomologicalComplex
import Mathlib.CategoryTheory.DifferentialObject
+#align_import algebra.homology.differential_object from "leanprover-community/mathlib"@"b535c2d5d996acd9b0554b76395d9c920e186f4f"
+
/-!
# Homological complexes are differential graded objects.
This is the second half of the changes originally in #5699, removing all occurrences of ;
after a space and implementing a linter rule to enforce it.
In most cases this 2-character substring has a space after it, so the following command was run first:
find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;
The remaining cases were few enough in number that they were done manually.
@@ -94,9 +94,9 @@ def dgoToHomologicalComplex :
{ X := fun i => X.obj i
d := fun i j =>
if h : i + b = j then X.d i ≫ X.objEqToHom (show i + (1 : ℤ) • b = j by simp [h]) else 0
- shape := fun i j w => by dsimp at w ; convert dif_neg w
+ shape := fun i j w => by dsimp at w; convert dif_neg w
d_comp_d' := fun i j k hij hjk => by
- dsimp at hij hjk ; substs hij hjk
+ dsimp at hij hjk; substs hij hjk
simp }
map {X Y} f :=
{ f := f.f
The unported dependencies are