algebra.category.Module.biproducts ⟷ Mathlib.Algebra.Category.ModuleCat.Biproducts

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

@@ -3,9 +3,9 @@ Copyright (c) 2022 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Algebra.Group.Pi
+import Algebra.Group.Pi.Lemmas
 import CategoryTheory.Limits.Shapes.Biproducts
-import Algebra.Category.Module.Abelian
+import Algebra.Category.ModuleCat.Abelian
 import Algebra.Homology.ShortExact.Abelian
 
 #align_import algebra.category.Module.biproducts from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"

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

@@ -3,10 +3,10 @@ Copyright (c) 2022 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Algebra.Group.Pi
-import Mathbin.CategoryTheory.Limits.Shapes.Biproducts
-import Mathbin.Algebra.Category.Module.Abelian
-import Mathbin.Algebra.Homology.ShortExact.Abelian
+import Algebra.Group.Pi
+import CategoryTheory.Limits.Shapes.Biproducts
+import Algebra.Category.Module.Abelian
+import Algebra.Homology.ShortExact.Abelian
 
 #align_import algebra.category.Module.biproducts from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 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.category.Module.biproducts
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Group.Pi
 import Mathbin.CategoryTheory.Limits.Shapes.Biproducts
 import Mathbin.Algebra.Category.Module.Abelian
 import Mathbin.Algebra.Homology.ShortExact.Abelian
 
+#align_import algebra.category.Module.biproducts from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # The category of `R`-modules has finite biproducts
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -141,7 +141,7 @@ def productLimitCone : Limits.LimitCone (Discrete.functor f)
     { lift := lift f
       fac := fun s j => by cases j; ext; simp
       uniq := fun s m w => by
-        ext (x j)
+        ext x j
         dsimp only [has_limit.lift]
         simp only [LinearMap.coe_mk]
         exact congr_arg (fun g : s.X ⟶ f j => (g : s.X → f j) x) (w ⟨j⟩) }

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

@@ -68,18 +68,23 @@ def binaryProductLimitCone (M N : ModuleCat.{v} R) : Limits.LimitCone (pair M N)
 #align Module.binary_product_limit_cone ModuleCat.binaryProductLimitCone
 -/
 
+#print ModuleCat.binaryProductLimitCone_cone_π_app_left /-
 @[simp]
 theorem binaryProductLimitCone_cone_π_app_left (M N : ModuleCat.{v} R) :
     (binaryProductLimitCone M N).Cone.π.app ⟨WalkingPair.left⟩ = LinearMap.fst R M N :=
   rfl
 #align Module.binary_product_limit_cone_cone_π_app_left ModuleCat.binaryProductLimitCone_cone_π_app_left
+-/
 
+#print ModuleCat.binaryProductLimitCone_cone_π_app_right /-
 @[simp]
 theorem binaryProductLimitCone_cone_π_app_right (M N : ModuleCat.{v} R) :
     (binaryProductLimitCone M N).Cone.π.app ⟨WalkingPair.right⟩ = LinearMap.snd R M N :=
   rfl
 #align Module.binary_product_limit_cone_cone_π_app_right ModuleCat.binaryProductLimitCone_cone_π_app_right
+-/
 
+#print ModuleCat.biprodIsoProd /-
 /-- We verify that the biproduct in `Module R` is isomorphic to
 the cartesian product of the underlying types:
 -/
@@ -88,18 +93,23 @@ noncomputable def biprodIsoProd (M N : ModuleCat.{v} R) :
     (M ⊞ N : ModuleCat.{v} R) ≅ ModuleCat.of R (M × N) :=
   IsLimit.conePointUniqueUpToIso (BinaryBiproduct.isLimit M N) (binaryProductLimitCone M N).IsLimit
 #align Module.biprod_iso_prod ModuleCat.biprodIsoProd
+-/
 
+#print ModuleCat.biprodIsoProd_inv_comp_fst /-
 @[simp, elementwise]
 theorem biprodIsoProd_inv_comp_fst (M N : ModuleCat.{v} R) :
     (biprodIsoProd M N).inv ≫ biprod.fst = LinearMap.fst R M N :=
   IsLimit.conePointUniqueUpToIso_inv_comp _ _ (Discrete.mk WalkingPair.left)
 #align Module.biprod_iso_prod_inv_comp_fst ModuleCat.biprodIsoProd_inv_comp_fst
+-/
 
+#print ModuleCat.biprodIsoProd_inv_comp_snd /-
 @[simp, elementwise]
 theorem biprodIsoProd_inv_comp_snd (M N : ModuleCat.{v} R) :
     (biprodIsoProd M N).inv ≫ biprod.snd = LinearMap.snd R M N :=
   IsLimit.conePointUniqueUpToIso_inv_comp _ _ (Discrete.mk WalkingPair.right)
 #align Module.biprod_iso_prod_inv_comp_snd ModuleCat.biprodIsoProd_inv_comp_snd
+-/
 
 namespace HasLimit
 
@@ -144,6 +154,7 @@ open HasLimit
 
 variable {J : Type} (f : J → ModuleCat.{v} R)
 
+#print ModuleCat.biproductIsoPi /-
 /-- We verify that the biproduct we've just defined is isomorphic to the `Module R` structure
 on the dependent function type
 -/
@@ -152,12 +163,15 @@ noncomputable def biproductIsoPi [Fintype J] (f : J → ModuleCat.{v} R) :
     (⨁ f : ModuleCat.{v} R) ≅ ModuleCat.of R (∀ j, f j) :=
   IsLimit.conePointUniqueUpToIso (biproduct.isLimit f) (productLimitCone f).IsLimit
 #align Module.biproduct_iso_pi ModuleCat.biproductIsoPi
+-/
 
+#print ModuleCat.biproductIsoPi_inv_comp_π /-
 @[simp, elementwise]
 theorem biproductIsoPi_inv_comp_π [Fintype J] (f : J → ModuleCat.{v} R) (j : J) :
     (biproductIsoPi f).inv ≫ biproduct.π f j = (LinearMap.proj j : (∀ j, f j) →ₗ[R] f j) :=
   IsLimit.conePointUniqueUpToIso_inv_comp _ _ (Discrete.mk j)
 #align Module.biproduct_iso_pi_inv_comp_π ModuleCat.biproductIsoPi_inv_comp_π
+-/
 
 end ModuleCat
 
@@ -170,6 +184,7 @@ variable {j : A →ₗ[R] M} {g : M →ₗ[R] B}
 
 open ModuleCat
 
+#print lequivProdOfRightSplitExact /-
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a right split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
 of modules.-/
 noncomputable def lequivProdOfRightSplitExact {f : B →ₗ[R] M} (hj : Function.Injective j)
@@ -179,7 +194,9 @@ noncomputable def lequivProdOfRightSplitExact {f : B →ₗ[R] M} (hj : Function
                   exact := (exact_iff _ _).mpr exac } : RightSplit _ _).Splitting.Iso.trans <|
         biprodIsoProd _ _).toLinearEquiv.symm
 #align lequiv_prod_of_right_split_exact lequivProdOfRightSplitExact
+-/
 
+#print lequivProdOfLeftSplitExact /-
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a left split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
 of modules.-/
 noncomputable def lequivProdOfLeftSplitExact {f : M →ₗ[R] A} (hg : Function.Surjective g)
@@ -189,6 +206,7 @@ noncomputable def lequivProdOfLeftSplitExact {f : M →ₗ[R] A} (hg : Function.
                   exact := (exact_iff _ _).mpr exac } : LeftSplit _ _).Splitting.Iso.trans <|
         biprodIsoProd _ _).toLinearEquiv.symm
 #align lequiv_prod_of_left_split_exact lequivProdOfLeftSplitExact
+-/
 
 end SplitExact
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -64,7 +64,7 @@ def binaryProductLimitCone (M N : ModuleCat.{v} R) : Limits.LimitCone (pair M N)
               Function.comp_apply, LinearMap.fst_apply, LinearMap.snd_apply, LinearMap.prod_apply,
               Pi.prod]
       uniq := fun s m w => by
-        ext <;> [rw [← w ⟨walking_pair.left⟩];rw [← w ⟨walking_pair.right⟩]] <;> rfl }
+        ext <;> [rw [← w ⟨walking_pair.left⟩]; rw [← w ⟨walking_pair.right⟩]] <;> rfl }
 #align Module.binary_product_limit_cone ModuleCat.binaryProductLimitCone
 -/
 

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

@@ -25,7 +25,7 @@ open CategoryTheory
 
 open CategoryTheory.Limits
 
-open BigOperators
+open scoped BigOperators
 
 universe w v u
 

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

@@ -68,30 +68,18 @@ def binaryProductLimitCone (M N : ModuleCat.{v} R) : Limits.LimitCone (pair M N)
 #align Module.binary_product_limit_cone ModuleCat.binaryProductLimitCone
 -/
 
-/- warning: Module.binary_product_limit_cone_cone_π_app_left -> ModuleCat.binaryProductLimitCone_cone_π_app_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Module.binary_product_limit_cone_cone_π_app_left ModuleCat.binaryProductLimitCone_cone_π_app_leftₓ'. -/
 @[simp]
 theorem binaryProductLimitCone_cone_π_app_left (M N : ModuleCat.{v} R) :
     (binaryProductLimitCone M N).Cone.π.app ⟨WalkingPair.left⟩ = LinearMap.fst R M N :=
   rfl
 #align Module.binary_product_limit_cone_cone_π_app_left ModuleCat.binaryProductLimitCone_cone_π_app_left
 
-/- warning: Module.binary_product_limit_cone_cone_π_app_right -> ModuleCat.binaryProductLimitCone_cone_π_app_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Module.binary_product_limit_cone_cone_π_app_right ModuleCat.binaryProductLimitCone_cone_π_app_rightₓ'. -/
 @[simp]
 theorem binaryProductLimitCone_cone_π_app_right (M N : ModuleCat.{v} R) :
     (binaryProductLimitCone M N).Cone.π.app ⟨WalkingPair.right⟩ = LinearMap.snd R M N :=
   rfl
 #align Module.binary_product_limit_cone_cone_π_app_right ModuleCat.binaryProductLimitCone_cone_π_app_right
 
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 /-- We verify that the biproduct in `Module R` is isomorphic to
 the cartesian product of the underlying types:
 -/
@@ -101,18 +89,12 @@ noncomputable def biprodIsoProd (M N : ModuleCat.{v} R) :
   IsLimit.conePointUniqueUpToIso (BinaryBiproduct.isLimit M N) (binaryProductLimitCone M N).IsLimit
 #align Module.biprod_iso_prod ModuleCat.biprodIsoProd
 
-/- warning: Module.biprod_iso_prod_inv_comp_fst -> ModuleCat.biprodIsoProd_inv_comp_fst is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Module.biprod_iso_prod_inv_comp_fst ModuleCat.biprodIsoProd_inv_comp_fstₓ'. -/
 @[simp, elementwise]
 theorem biprodIsoProd_inv_comp_fst (M N : ModuleCat.{v} R) :
     (biprodIsoProd M N).inv ≫ biprod.fst = LinearMap.fst R M N :=
   IsLimit.conePointUniqueUpToIso_inv_comp _ _ (Discrete.mk WalkingPair.left)
 #align Module.biprod_iso_prod_inv_comp_fst ModuleCat.biprodIsoProd_inv_comp_fst
 
-/- warning: Module.biprod_iso_prod_inv_comp_snd -> ModuleCat.biprodIsoProd_inv_comp_snd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Module.biprod_iso_prod_inv_comp_snd ModuleCat.biprodIsoProd_inv_comp_sndₓ'. -/
 @[simp, elementwise]
 theorem biprodIsoProd_inv_comp_snd (M N : ModuleCat.{v} R) :
     (biprodIsoProd M N).inv ≫ biprod.snd = LinearMap.snd R M N :=
@@ -162,12 +144,6 @@ open HasLimit
 
 variable {J : Type} (f : J → ModuleCat.{v} R)
 
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 /-- We verify that the biproduct we've just defined is isomorphic to the `Module R` structure
 on the dependent function type
 -/
@@ -177,9 +153,6 @@ noncomputable def biproductIsoPi [Fintype J] (f : J → ModuleCat.{v} R) :
   IsLimit.conePointUniqueUpToIso (biproduct.isLimit f) (productLimitCone f).IsLimit
 #align Module.biproduct_iso_pi ModuleCat.biproductIsoPi
 
-/- warning: Module.biproduct_iso_pi_inv_comp_π -> ModuleCat.biproductIsoPi_inv_comp_π is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Module.biproduct_iso_pi_inv_comp_π ModuleCat.biproductIsoPi_inv_comp_πₓ'. -/
 @[simp, elementwise]
 theorem biproductIsoPi_inv_comp_π [Fintype J] (f : J → ModuleCat.{v} R) (j : J) :
     (biproductIsoPi f).inv ≫ biproduct.π f j = (LinearMap.proj j : (∀ j, f j) →ₗ[R] f j) :=
@@ -197,9 +170,6 @@ variable {j : A →ₗ[R] M} {g : M →ₗ[R] B}
 
 open ModuleCat
 
-/- warning: lequiv_prod_of_right_split_exact -> lequivProdOfRightSplitExact is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lequiv_prod_of_right_split_exact lequivProdOfRightSplitExactₓ'. -/
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a right split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
 of modules.-/
 noncomputable def lequivProdOfRightSplitExact {f : B →ₗ[R] M} (hj : Function.Injective j)
@@ -210,9 +180,6 @@ noncomputable def lequivProdOfRightSplitExact {f : B →ₗ[R] M} (hj : Function
         biprodIsoProd _ _).toLinearEquiv.symm
 #align lequiv_prod_of_right_split_exact lequivProdOfRightSplitExact
 
-/- warning: lequiv_prod_of_left_split_exact -> lequivProdOfLeftSplitExact is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lequiv_prod_of_left_split_exact lequivProdOfLeftSplitExactₓ'. -/
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a left split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
 of modules.-/
 noncomputable def lequivProdOfLeftSplitExact {f : M →ₗ[R] A} (hg : Function.Surjective g)

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

@@ -59,7 +59,7 @@ def binaryProductLimitCone (M N : ModuleCat.{v} R) : Limits.LimitCone (pair M N)
     { lift := fun s => LinearMap.prod (s.π.app ⟨WalkingPair.left⟩) (s.π.app ⟨WalkingPair.right⟩)
       fac := by
         rintro s (⟨⟩ | ⟨⟩) <;>
-          · ext x
+          · ext x;
             simp only [binary_fan.π_app_right, binary_fan.π_app_left, ModuleCat.coe_comp,
               Function.comp_apply, LinearMap.fst_apply, LinearMap.snd_apply, LinearMap.prod_apply,
               Pi.prod]
@@ -131,12 +131,8 @@ to the cartesian product of those groups.
 def lift (s : Fan f) : s.pt ⟶ ModuleCat.of R (∀ j, f j)
     where
   toFun x j := s.π.app ⟨j⟩ x
-  map_add' x y := by
-    ext
-    simp
-  map_smul' r x := by
-    ext
-    simp
+  map_add' x y := by ext; simp
+  map_smul' r x := by ext; simp
 #align Module.has_limit.lift ModuleCat.HasLimit.lift
 -/
 
@@ -151,10 +147,7 @@ def productLimitCone : Limits.LimitCone (Discrete.functor f)
       π := Discrete.natTrans fun j => (LinearMap.proj j.as : (∀ j, f j) →ₗ[R] f j.as) }
   IsLimit :=
     { lift := lift f
-      fac := fun s j => by
-        cases j
-        ext
-        simp
+      fac := fun s j => by cases j; ext; simp
       uniq := fun s m w => by
         ext (x j)
         dsimp only [has_limit.lift]

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

@@ -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.category.Module.biproducts
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Algebra.Homology.ShortExact.Abelian
 
 /-!
 # The category of `R`-modules has finite biproducts
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/
 
 
@@ -66,10 +69,7 @@ def binaryProductLimitCone (M N : ModuleCat.{v} R) : Limits.LimitCone (pair M N)
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Module.binary_product_limit_cone_cone_π_app_left ModuleCat.binaryProductLimitCone_cone_π_app_leftₓ'. -/
 @[simp]
 theorem binaryProductLimitCone_cone_π_app_left (M N : ModuleCat.{v} R) :
@@ -78,10 +78,7 @@ theorem binaryProductLimitCone_cone_π_app_left (M N : ModuleCat.{v} R) :
 #align Module.binary_product_limit_cone_cone_π_app_left ModuleCat.binaryProductLimitCone_cone_π_app_left
 
 /- warning: Module.binary_product_limit_cone_cone_π_app_right -> ModuleCat.binaryProductLimitCone_cone_π_app_right is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align Module.binary_product_limit_cone_cone_π_app_right ModuleCat.binaryProductLimitCone_cone_π_app_rightₓ'. -/
 @[simp]
 theorem binaryProductLimitCone_cone_π_app_right (M N : ModuleCat.{v} R) :
@@ -105,10 +102,7 @@ noncomputable def biprodIsoProd (M N : ModuleCat.{v} R) :
 #align Module.biprod_iso_prod ModuleCat.biprodIsoProd
 
 /- warning: Module.biprod_iso_prod_inv_comp_fst -> ModuleCat.biprodIsoProd_inv_comp_fst is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align Module.biprod_iso_prod_inv_comp_fst ModuleCat.biprodIsoProd_inv_comp_fstₓ'. -/
 @[simp, elementwise]
 theorem biprodIsoProd_inv_comp_fst (M N : ModuleCat.{v} R) :
@@ -117,10 +111,7 @@ theorem biprodIsoProd_inv_comp_fst (M N : ModuleCat.{v} R) :
 #align Module.biprod_iso_prod_inv_comp_fst ModuleCat.biprodIsoProd_inv_comp_fst
 
 /- warning: Module.biprod_iso_prod_inv_comp_snd -> ModuleCat.biprodIsoProd_inv_comp_snd is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align Module.biprod_iso_prod_inv_comp_snd ModuleCat.biprodIsoProd_inv_comp_sndₓ'. -/
 @[simp, elementwise]
 theorem biprodIsoProd_inv_comp_snd (M N : ModuleCat.{v} R) :
@@ -194,10 +185,7 @@ noncomputable def biproductIsoPi [Fintype J] (f : J → ModuleCat.{v} R) :
 #align Module.biproduct_iso_pi ModuleCat.biproductIsoPi
 
 /- warning: Module.biproduct_iso_pi_inv_comp_π -> ModuleCat.biproductIsoPi_inv_comp_π is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align Module.biproduct_iso_pi_inv_comp_π ModuleCat.biproductIsoPi_inv_comp_πₓ'. -/
 @[simp, elementwise]
 theorem biproductIsoPi_inv_comp_π [Fintype J] (f : J → ModuleCat.{v} R) (j : J) :
@@ -217,10 +205,7 @@ variable {j : A →ₗ[R] M} {g : M →ₗ[R] B}
 open ModuleCat
 
 /- warning: lequiv_prod_of_right_split_exact -> lequivProdOfRightSplitExact is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align lequiv_prod_of_right_split_exact lequivProdOfRightSplitExactₓ'. -/
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a right split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
 of modules.-/
@@ -233,10 +218,7 @@ noncomputable def lequivProdOfRightSplitExact {f : B →ₗ[R] M} (hj : Function
 #align lequiv_prod_of_right_split_exact lequivProdOfRightSplitExact
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lequiv_prod_of_left_split_exact lequivProdOfLeftSplitExactₓ'. -/
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a left split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
 of modules.-/

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

@@ -37,6 +37,7 @@ instance : HasBinaryBiproducts (ModuleCat.{v} R) :=
 instance : HasFiniteBiproducts (ModuleCat.{v} R) :=
   HasFiniteBiproducts.of_hasFiniteProducts
 
+#print ModuleCat.binaryProductLimitCone /-
 -- We now construct explicit limit data,
 -- so we can compare the biproducts to the usual unbundled constructions.
 /-- Construct limit data for a binary product in `Module R`, using `Module.of R (M × N)`.
@@ -62,19 +63,38 @@ def binaryProductLimitCone (M N : ModuleCat.{v} R) : Limits.LimitCone (pair M N)
       uniq := fun s m w => by
         ext <;> [rw [← w ⟨walking_pair.left⟩];rw [← w ⟨walking_pair.right⟩]] <;> rfl }
 #align Module.binary_product_limit_cone ModuleCat.binaryProductLimitCone
+-/
 
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+Case conversion may be inaccurate. Consider using '#align Module.binary_product_limit_cone_cone_π_app_left ModuleCat.binaryProductLimitCone_cone_π_app_leftₓ'. -/
 @[simp]
 theorem binaryProductLimitCone_cone_π_app_left (M N : ModuleCat.{v} R) :
     (binaryProductLimitCone M N).Cone.π.app ⟨WalkingPair.left⟩ = LinearMap.fst R M N :=
   rfl
 #align Module.binary_product_limit_cone_cone_π_app_left ModuleCat.binaryProductLimitCone_cone_π_app_left
 
+/- warning: Module.binary_product_limit_cone_cone_π_app_right -> ModuleCat.binaryProductLimitCone_cone_π_app_right is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align Module.binary_product_limit_cone_cone_π_app_right ModuleCat.binaryProductLimitCone_cone_π_app_rightₓ'. -/
 @[simp]
 theorem binaryProductLimitCone_cone_π_app_right (M N : ModuleCat.{v} R) :
     (binaryProductLimitCone M N).Cone.π.app ⟨WalkingPair.right⟩ = LinearMap.snd R M N :=
   rfl
 #align Module.binary_product_limit_cone_cone_π_app_right ModuleCat.binaryProductLimitCone_cone_π_app_right
 
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+Case conversion may be inaccurate. Consider using '#align Module.biprod_iso_prod ModuleCat.biprodIsoProdₓ'. -/
 /-- We verify that the biproduct in `Module R` is isomorphic to
 the cartesian product of the underlying types:
 -/
@@ -84,12 +104,24 @@ noncomputable def biprodIsoProd (M N : ModuleCat.{v} R) :
   IsLimit.conePointUniqueUpToIso (BinaryBiproduct.isLimit M N) (binaryProductLimitCone M N).IsLimit
 #align Module.biprod_iso_prod ModuleCat.biprodIsoProd
 
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+Case conversion may be inaccurate. Consider using '#align Module.biprod_iso_prod_inv_comp_fst ModuleCat.biprodIsoProd_inv_comp_fstₓ'. -/
 @[simp, elementwise]
 theorem biprodIsoProd_inv_comp_fst (M N : ModuleCat.{v} R) :
     (biprodIsoProd M N).inv ≫ biprod.fst = LinearMap.fst R M N :=
   IsLimit.conePointUniqueUpToIso_inv_comp _ _ (Discrete.mk WalkingPair.left)
 #align Module.biprod_iso_prod_inv_comp_fst ModuleCat.biprodIsoProd_inv_comp_fst
 
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+Case conversion may be inaccurate. Consider using '#align Module.biprod_iso_prod_inv_comp_snd ModuleCat.biprodIsoProd_inv_comp_sndₓ'. -/
 @[simp, elementwise]
 theorem biprodIsoProd_inv_comp_snd (M N : ModuleCat.{v} R) :
     (biprodIsoProd M N).inv ≫ biprod.snd = LinearMap.snd R M N :=
@@ -100,6 +132,7 @@ namespace HasLimit
 
 variable {J : Type w} (f : J → ModuleCat.{max w v} R)
 
+#print ModuleCat.HasLimit.lift /-
 /-- The map from an arbitrary cone over a indexed family of abelian groups
 to the cartesian product of those groups.
 -/
@@ -114,7 +147,9 @@ def lift (s : Fan f) : s.pt ⟶ ModuleCat.of R (∀ j, f j)
     ext
     simp
 #align Module.has_limit.lift ModuleCat.HasLimit.lift
+-/
 
+#print ModuleCat.HasLimit.productLimitCone /-
 /-- Construct limit data for a product in `Module R`, using `Module.of R (Π j, F.obj j)`.
 -/
 @[simps]
@@ -135,6 +170,7 @@ def productLimitCone : Limits.LimitCone (Discrete.functor f)
         simp only [LinearMap.coe_mk]
         exact congr_arg (fun g : s.X ⟶ f j => (g : s.X → f j) x) (w ⟨j⟩) }
 #align Module.has_limit.product_limit_cone ModuleCat.HasLimit.productLimitCone
+-/
 
 end HasLimit
 
@@ -142,6 +178,12 @@ open HasLimit
 
 variable {J : Type} (f : J → ModuleCat.{v} R)
 
+/- warning: Module.biproduct_iso_pi -> ModuleCat.biproductIsoPi is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align Module.biproduct_iso_pi ModuleCat.biproductIsoPiₓ'. -/
 /-- We verify that the biproduct we've just defined is isomorphic to the `Module R` structure
 on the dependent function type
 -/
@@ -151,6 +193,12 @@ noncomputable def biproductIsoPi [Fintype J] (f : J → ModuleCat.{v} R) :
   IsLimit.conePointUniqueUpToIso (biproduct.isLimit f) (productLimitCone f).IsLimit
 #align Module.biproduct_iso_pi ModuleCat.biproductIsoPi
 
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+Case conversion may be inaccurate. Consider using '#align Module.biproduct_iso_pi_inv_comp_π ModuleCat.biproductIsoPi_inv_comp_πₓ'. -/
 @[simp, elementwise]
 theorem biproductIsoPi_inv_comp_π [Fintype J] (f : J → ModuleCat.{v} R) (j : J) :
     (biproductIsoPi f).inv ≫ biproduct.π f j = (LinearMap.proj j : (∀ j, f j) →ₗ[R] f j) :=
@@ -168,6 +216,12 @@ variable {j : A →ₗ[R] M} {g : M →ₗ[R] B}
 
 open ModuleCat
 
+/- warning: lequiv_prod_of_right_split_exact -> lequivProdOfRightSplitExact is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align lequiv_prod_of_right_split_exact lequivProdOfRightSplitExactₓ'. -/
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a right split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
 of modules.-/
 noncomputable def lequivProdOfRightSplitExact {f : B →ₗ[R] M} (hj : Function.Injective j)
@@ -178,6 +232,12 @@ noncomputable def lequivProdOfRightSplitExact {f : B →ₗ[R] M} (hj : Function
         biprodIsoProd _ _).toLinearEquiv.symm
 #align lequiv_prod_of_right_split_exact lequivProdOfRightSplitExact
 
+/- warning: lequiv_prod_of_left_split_exact -> lequivProdOfLeftSplitExact is a dubious translation:
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(Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} B _inst_4) _inst_7 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_6) _inst_7) (LinearMap.range.{u2, u2, u1, u1, u1} R R A M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_6) _inst_3 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) A M (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R A M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_6) _inst_3 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) j) (LinearMap.ker.{u2, u2, u1, u1, u1} R R M B (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} B _inst_4) _inst_7 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M B (AddCommGroup.toAddCommMonoid.{u1} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} B _inst_4) _inst_7 _inst_5) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M B (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} B _inst_4) _inst_7 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) A A (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) _inst_3 _inst_3) (LinearMap.comp.{u2, u2, u2, u1, u1, u1} R R R A M A (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) _inst_3 _inst_7 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f j) (LinearMap.id.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) _inst_3)) -> (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Prod.{u1, u1} A B) M (Prod.instAddCommMonoidSum.{u1, u1} A B (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) (AddCommGroup.toAddCommMonoid.{u1} B _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_6) (Prod.module.{u2, u1, u1} R A B (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) (AddCommGroup.toAddCommMonoid.{u1} B _inst_4) _inst_3 _inst_5) _inst_7)
+Case conversion may be inaccurate. Consider using '#align lequiv_prod_of_left_split_exact lequivProdOfLeftSplitExactₓ'. -/
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a left split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
 of modules.-/
 noncomputable def lequivProdOfLeftSplitExact {f : M →ₗ[R] A} (hg : Function.Surjective g)

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -60,7 +60,7 @@ def binaryProductLimitCone (M N : ModuleCat.{v} R) : Limits.LimitCone (pair M N)
               Function.comp_apply, LinearMap.fst_apply, LinearMap.snd_apply, LinearMap.prod_apply,
               Pi.prod]
       uniq := fun s m w => by
-        ext <;> [rw [← w ⟨walking_pair.left⟩], rw [← w ⟨walking_pair.right⟩]] <;> rfl }
+        ext <;> [rw [← w ⟨walking_pair.left⟩];rw [← w ⟨walking_pair.right⟩]] <;> rfl }
 #align Module.binary_product_limit_cone ModuleCat.binaryProductLimitCone
 
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,13 +4,12 @@ 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.category.Module.biproducts
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Group.Pi
 import Mathbin.CategoryTheory.Limits.Shapes.Biproducts
-import Mathbin.Algebra.Category.Module.Limits
 import Mathbin.Algebra.Category.Module.Abelian
 import Mathbin.Algebra.Homology.ShortExact.Abelian
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

@@ -149,7 +149,7 @@ on the dependent function type
 @[simps hom_apply]
 noncomputable def biproductIsoPi [Fintype J] (f : J → ModuleCat.{v} R) :
     (⨁ f : ModuleCat.{v} R) ≅ ModuleCat.of R (∀ j, f j) :=
-  IsLimit.conePointUniqueUpToIso (Biproduct.isLimit f) (productLimitCone f).IsLimit
+  IsLimit.conePointUniqueUpToIso (biproduct.isLimit f) (productLimitCone f).IsLimit
 #align Module.biproduct_iso_pi ModuleCat.biproductIsoPi
 
 @[simp, elementwise]

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -46,7 +46,7 @@ instance : HasFiniteBiproducts (ModuleCat.{v} R) :=
 def binaryProductLimitCone (M N : ModuleCat.{v} R) : Limits.LimitCone (pair M N)
     where
   Cone :=
-    { x := ModuleCat.of R (M × N)
+    { pt := ModuleCat.of R (M × N)
       π :=
         { app := fun j =>
             Discrete.casesOn j fun j =>
@@ -105,7 +105,7 @@ variable {J : Type w} (f : J → ModuleCat.{max w v} R)
 to the cartesian product of those groups.
 -/
 @[simps]
-def lift (s : Fan f) : s.x ⟶ ModuleCat.of R (∀ j, f j)
+def lift (s : Fan f) : s.pt ⟶ ModuleCat.of R (∀ j, f j)
     where
   toFun x j := s.π.app ⟨j⟩ x
   map_add' x y := by
@@ -122,7 +122,7 @@ def lift (s : Fan f) : s.x ⟶ ModuleCat.of R (∀ j, f j)
 def productLimitCone : Limits.LimitCone (Discrete.functor f)
     where
   Cone :=
-    { x := ModuleCat.of R (∀ j, f j)
+    { pt := ModuleCat.of R (∀ j, f j)
       π := Discrete.natTrans fun j => (LinearMap.proj j.as : (∀ j, f j) →ₗ[R] f j.as) }
   IsLimit :=
     { lift := lift f

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -33,10 +33,10 @@ variable {R : Type u} [Ring R]
 
 -- As `Module R` is preadditive, and has all limits, it automatically has biproducts.
 instance : HasBinaryBiproducts (ModuleCat.{v} R) :=
-  HasBinaryBiproducts.ofHasBinaryProducts
+  HasBinaryBiproducts.of_hasBinaryProducts
 
 instance : HasFiniteBiproducts (ModuleCat.{v} R) :=
-  HasFiniteBiproducts.ofHasFiniteProducts
+  HasFiniteBiproducts.of_hasFiniteProducts
 
 -- We now construct explicit limit data,
 -- so we can compare the biproducts to the usual unbundled constructions.
@@ -54,13 +54,13 @@ def binaryProductLimitCone (M N : ModuleCat.{v} R) : Limits.LimitCone (pair M N)
           naturality' := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨⟨⟨⟩⟩⟩ <;> rfl } }
   IsLimit :=
     { lift := fun s => LinearMap.prod (s.π.app ⟨WalkingPair.left⟩) (s.π.app ⟨WalkingPair.right⟩)
-      fac' := by
+      fac := by
         rintro s (⟨⟩ | ⟨⟩) <;>
           · ext x
             simp only [binary_fan.π_app_right, binary_fan.π_app_left, ModuleCat.coe_comp,
               Function.comp_apply, LinearMap.fst_apply, LinearMap.snd_apply, LinearMap.prod_apply,
               Pi.prod]
-      uniq' := fun s m w => by
+      uniq := fun s m w => by
         ext <;> [rw [← w ⟨walking_pair.left⟩], rw [← w ⟨walking_pair.right⟩]] <;> rfl }
 #align Module.binary_product_limit_cone ModuleCat.binaryProductLimitCone
 
@@ -126,11 +126,11 @@ def productLimitCone : Limits.LimitCone (Discrete.functor f)
       π := Discrete.natTrans fun j => (LinearMap.proj j.as : (∀ j, f j) →ₗ[R] f j.as) }
   IsLimit :=
     { lift := lift f
-      fac' := fun s j => by
+      fac := fun s j => by
         cases j
         ext
         simp
-      uniq' := fun s m w => by
+      uniq := fun s m w => by
         ext (x j)
         dsimp only [has_limit.lift]
         simp only [LinearMap.coe_mk]

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

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

@@ -163,7 +163,7 @@ open ModuleCat
 
 
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a right split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
-of modules.-/
+of modules. -/
 noncomputable def lequivProdOfRightSplitExact {f : B →ₗ[R] M} (hj : Function.Injective j)
     (exac : LinearMap.range j = LinearMap.ker g) (h : g.comp f = LinearMap.id) : (A × B) ≃ₗ[R] M :=
   ((ShortComplex.Splitting.ofExactOfSection _
@@ -173,7 +173,7 @@ noncomputable def lequivProdOfRightSplitExact {f : B →ₗ[R] M} (hj : Function
     biprodIsoProd _ _ ).symm.toLinearEquiv
 
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a left split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
-of modules.-/
+of modules. -/
 noncomputable def lequivProdOfLeftSplitExact {f : M →ₗ[R] A} (hg : Function.Surjective g)
     (exac : LinearMap.range j = LinearMap.ker g) (h : f.comp j = LinearMap.id) : (A × B) ≃ₗ[R] M :=
   ((ShortComplex.Splitting.ofExactOfRetraction _

Rename

• Data.Pi.Algebra to Algebra.Group.Pi.Basic
• Algebra.Group.Pi to Algebra.Group.Pi.Lemmas

Move a few instances from the latter to the former, the goal being that Algebra.Group.Pi.Basic is about all the pi instances of the classes defined in Algebra.Group.Defs. Algebra.Group.Pi.Lemmas will need further rearranging.

@@ -3,7 +3,7 @@ Copyright (c) 2022 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathlib.Algebra.Group.Pi
+import Mathlib.Algebra.Group.Pi.Lemmas
 import Mathlib.CategoryTheory.Limits.Shapes.Biproducts
 import Mathlib.Algebra.Category.ModuleCat.Abelian
 import Mathlib.Algebra.Homology.ShortComplex.ModuleCat

@@ -136,7 +136,7 @@ variable {J : Type} (f : J → ModuleCat.{v} R)
 on the dependent function type.
 -/
 @[simps! hom_apply]
-noncomputable def biproductIsoPi [Fintype J] (f : J → ModuleCat.{v} R) :
+noncomputable def biproductIsoPi [Finite J] (f : J → ModuleCat.{v} R) :
     ((⨁ f) : ModuleCat.{v} R) ≅ ModuleCat.of R (∀ j, f j) :=
   IsLimit.conePointUniqueUpToIso (biproduct.isLimit f) (productLimitCone f).isLimit
 #align Module.biproduct_iso_pi ModuleCat.biproductIsoPi
@@ -145,7 +145,7 @@ noncomputable def biproductIsoPi [Fintype J] (f : J → ModuleCat.{v} R) :
 attribute [nolint simpNF] ModuleCat.biproductIsoPi_hom_apply
 
 @[simp, elementwise]
-theorem biproductIsoPi_inv_comp_π [Fintype J] (f : J → ModuleCat.{v} R) (j : J) :
+theorem biproductIsoPi_inv_comp_π [Finite J] (f : J → ModuleCat.{v} R) (j : J) :
     (biproductIsoPi f).inv ≫ biproduct.π f j = (LinearMap.proj j : (∀ j, f j) →ₗ[R] f j) :=
   IsLimit.conePointUniqueUpToIso_inv_comp _ _ (Discrete.mk j)
 #align Module.biproduct_iso_pi_inv_comp_π ModuleCat.biproductIsoPi_inv_comp_π

This PR refactors the four and the five lemmas so as to use the new homology API. The files Algebra.Homology.ShortExact.Abelian and Algebra.Homology.ShortExact.Preadditive are also removed because the content of these files has become redundant with the new homology API.

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

@@ -6,7 +6,7 @@ Authors: Scott Morrison
 import Mathlib.Algebra.Group.Pi
 import Mathlib.CategoryTheory.Limits.Shapes.Biproducts
 import Mathlib.Algebra.Category.ModuleCat.Abelian
-import Mathlib.Algebra.Homology.ShortExact.Abelian
+import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
 
 #align_import algebra.category.Module.biproducts from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
 
@@ -161,24 +161,26 @@ variable {j : A →ₗ[R] M} {g : M →ₗ[R] B}
 
 open ModuleCat
 
+
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a right split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
 of modules.-/
 noncomputable def lequivProdOfRightSplitExact {f : B →ₗ[R] M} (hj : Function.Injective j)
     (exac : LinearMap.range j = LinearMap.ker g) (h : g.comp f = LinearMap.id) : (A × B) ≃ₗ[R] M :=
-  (({ right_split := ⟨ModuleCat.asHom f, h⟩
-      mono := (ModuleCat.mono_iff_injective <| asHom j).mpr hj
-      exact := (exact_iff _ _).mpr exac } : RightSplit _ _).splitting.iso.trans <|
-    biprodIsoProd _ _).toLinearEquiv.symm
-#align lequiv_prod_of_right_split_exact lequivProdOfRightSplitExact
+  ((ShortComplex.Splitting.ofExactOfSection _
+    (ShortComplex.Exact.moduleCat_of_range_eq_ker (ModuleCat.ofHom j)
+    (ModuleCat.ofHom g) exac) (asHom f) h
+    (by simpa only [ModuleCat.mono_iff_injective])).isoBinaryBiproduct ≪≫
+    biprodIsoProd _ _ ).symm.toLinearEquiv
 
 /-- The isomorphism `A × B ≃ₗ[R] M` coming from a left split exact sequence `0 ⟶ A ⟶ M ⟶ B ⟶ 0`
 of modules.-/
 noncomputable def lequivProdOfLeftSplitExact {f : M →ₗ[R] A} (hg : Function.Surjective g)
     (exac : LinearMap.range j = LinearMap.ker g) (h : f.comp j = LinearMap.id) : (A × B) ≃ₗ[R] M :=
-  (({ left_split := ⟨ModuleCat.asHom f, h⟩
-      epi := (ModuleCat.epi_iff_surjective <| asHom g).mpr hg
-      exact := (exact_iff _ _).mpr exac } : LeftSplit _ _).splitting.iso.trans <|
-    biprodIsoProd _ _).toLinearEquiv.symm
+  ((ShortComplex.Splitting.ofExactOfRetraction _
+    (ShortComplex.Exact.moduleCat_of_range_eq_ker (ModuleCat.ofHom j)
+    (ModuleCat.ofHom g) exac) (ModuleCat.ofHom f) h
+    (by simpa only [ModuleCat.epi_iff_surjective] using hg)).isoBinaryBiproduct ≪≫
+    biprodIsoProd _ _).symm.toLinearEquiv
 #align lequiv_prod_of_left_split_exact lequivProdOfLeftSplitExact
 
 end SplitExact

This reverts commit f3695eb2.

@@ -77,6 +77,9 @@ noncomputable def biprodIsoProd (M N : ModuleCat.{v} R) :
   IsLimit.conePointUniqueUpToIso (BinaryBiproduct.isLimit M N) (binaryProductLimitCone M N).isLimit
 #align Module.biprod_iso_prod ModuleCat.biprodIsoProd
 
+-- These lemmas have always been bad (#7657), but lean4#2644 made `simp` start noticing
+attribute [nolint simpNF] ModuleCat.biprodIsoProd_hom_apply
+
 @[simp, elementwise]
 theorem biprodIsoProd_inv_comp_fst (M N : ModuleCat.{v} R) :
     (biprodIsoProd M N).inv ≫ biprod.fst = LinearMap.fst R M N :=
@@ -138,6 +141,9 @@ noncomputable def biproductIsoPi [Fintype J] (f : J → ModuleCat.{v} R) :
   IsLimit.conePointUniqueUpToIso (biproduct.isLimit f) (productLimitCone f).isLimit
 #align Module.biproduct_iso_pi ModuleCat.biproductIsoPi
 
+-- These lemmas have always been bad (#7657), but lean4#2644 made `simp` start noticing
+attribute [nolint simpNF] ModuleCat.biproductIsoPi_hom_apply
+
 @[simp, elementwise]
 theorem biproductIsoPi_inv_comp_π [Fintype J] (f : J → ModuleCat.{v} R) (j : J) :
     (biproductIsoPi f).inv ≫ biproduct.π f j = (LinearMap.proj j : (∀ j, f j) →ₗ[R] f j) :=

This reverts commit 26eb2b0a.

@@ -77,9 +77,6 @@ noncomputable def biprodIsoProd (M N : ModuleCat.{v} R) :
   IsLimit.conePointUniqueUpToIso (BinaryBiproduct.isLimit M N) (binaryProductLimitCone M N).isLimit
 #align Module.biprod_iso_prod ModuleCat.biprodIsoProd
 
--- These lemmas have always been bad (#7657), but lean4#2644 made `simp` start noticing
-attribute [nolint simpNF] ModuleCat.biprodIsoProd_hom_apply
-
 @[simp, elementwise]
 theorem biprodIsoProd_inv_comp_fst (M N : ModuleCat.{v} R) :
     (biprodIsoProd M N).inv ≫ biprod.fst = LinearMap.fst R M N :=
@@ -141,9 +138,6 @@ noncomputable def biproductIsoPi [Fintype J] (f : J → ModuleCat.{v} R) :
   IsLimit.conePointUniqueUpToIso (biproduct.isLimit f) (productLimitCone f).isLimit
 #align Module.biproduct_iso_pi ModuleCat.biproductIsoPi
 
--- These lemmas have always been bad (#7657), but lean4#2644 made `simp` start noticing
-attribute [nolint simpNF] ModuleCat.biproductIsoPi_hom_apply
-
 @[simp, elementwise]
 theorem biproductIsoPi_inv_comp_π [Fintype J] (f : J → ModuleCat.{v} R) (j : J) :
     (biproductIsoPi f).inv ≫ biproduct.π f j = (LinearMap.proj j : (∀ j, f j) →ₗ[R] f j) :=

This includes all the changes from #7606.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -77,6 +77,9 @@ noncomputable def biprodIsoProd (M N : ModuleCat.{v} R) :
   IsLimit.conePointUniqueUpToIso (BinaryBiproduct.isLimit M N) (binaryProductLimitCone M N).isLimit
 #align Module.biprod_iso_prod ModuleCat.biprodIsoProd
 
+-- These lemmas have always been bad (#7657), but lean4#2644 made `simp` start noticing
+attribute [nolint simpNF] ModuleCat.biprodIsoProd_hom_apply
+
 @[simp, elementwise]
 theorem biprodIsoProd_inv_comp_fst (M N : ModuleCat.{v} R) :
     (biprodIsoProd M N).inv ≫ biprod.fst = LinearMap.fst R M N :=
@@ -138,6 +141,9 @@ noncomputable def biproductIsoPi [Fintype J] (f : J → ModuleCat.{v} R) :
   IsLimit.conePointUniqueUpToIso (biproduct.isLimit f) (productLimitCone f).isLimit
 #align Module.biproduct_iso_pi ModuleCat.biproductIsoPi
 
+-- These lemmas have always been bad (#7657), but lean4#2644 made `simp` start noticing
+attribute [nolint simpNF] ModuleCat.biproductIsoPi_hom_apply
+
 @[simp, elementwise]
 theorem biproductIsoPi_inv_comp_π [Fintype J] (f : J → ModuleCat.{v} R) (j : J) :
     (biproductIsoPi f).inv ≫ biproduct.π f j = (LinearMap.proj j : (∀ j, f j) →ₗ[R] f j) :=

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 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.category.Module.biproducts
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Group.Pi
 import Mathlib.CategoryTheory.Limits.Shapes.Biproducts
 import Mathlib.Algebra.Category.ModuleCat.Abelian
 import Mathlib.Algebra.Homology.ShortExact.Abelian
 
+#align_import algebra.category.Module.biproducts from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # The category of `R`-modules has finite biproducts
 -/

All of these are doc fixes

@@ -96,7 +96,7 @@ namespace HasLimit
 
 variable {J : Type w} (f : J → ModuleCat.{max w v} R)
 
-/-- The map from an arbitrary cone over a indexed family of abelian groups
+/-- The map from an arbitrary cone over an indexed family of abelian groups
 to the cartesian product of those groups.
 -/
 @[simps]