category_theory.limits.shapes.finite_products
⟷
Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
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
@@ -29,7 +29,7 @@ namespace CategoryTheory.Limits
variable (C : Type u) [Category.{v} C]
#print CategoryTheory.Limits.HasFiniteProducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite products if there is a chosen limit for every diagram
with shape `discrete J`, where we have `[finite J]`.
@@ -72,7 +72,7 @@ theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts
-/
#print CategoryTheory.Limits.HasFiniteCoproducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite coproducts if there is a chosen colimit for every diagram
with shape `discrete J`, where we have `[fintype J]`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -29,7 +29,7 @@ namespace CategoryTheory.Limits
variable (C : Type u) [Category.{v} C]
#print CategoryTheory.Limits.HasFiniteProducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite products if there is a chosen limit for every diagram
with shape `discrete J`, where we have `[finite J]`.
@@ -72,7 +72,7 @@ theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts
-/
#print CategoryTheory.Limits.HasFiniteCoproducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite coproducts if there is a chosen colimit for every diagram
with shape `discrete J`, where we have `[fintype J]`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -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
-/
-import Mathbin.CategoryTheory.Limits.Shapes.FiniteLimits
-import Mathbin.CategoryTheory.Limits.Shapes.Products
+import CategoryTheory.Limits.Shapes.FiniteLimits
+import CategoryTheory.Limits.Shapes.Products
#align_import category_theory.limits.shapes.finite_products from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
@@ -29,7 +29,7 @@ namespace CategoryTheory.Limits
variable (C : Type u) [Category.{v} C]
#print CategoryTheory.Limits.HasFiniteProducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite products if there is a chosen limit for every diagram
with shape `discrete J`, where we have `[finite J]`.
@@ -72,7 +72,7 @@ theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts
-/
#print CategoryTheory.Limits.HasFiniteCoproducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite coproducts if there is a chosen colimit for every diagram
with shape `discrete J`, where we have `[fintype J]`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -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
-
-! This file was ported from Lean 3 source module category_theory.limits.shapes.finite_products
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Limits.Shapes.FiniteLimits
import Mathbin.CategoryTheory.Limits.Shapes.Products
+#align_import category_theory.limits.shapes.finite_products from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
/-!
# Categories with finite (co)products
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -32,7 +32,7 @@ namespace CategoryTheory.Limits
variable (C : Type u) [Category.{v} C]
#print CategoryTheory.Limits.HasFiniteProducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite products if there is a chosen limit for every diagram
with shape `discrete J`, where we have `[finite J]`.
@@ -75,7 +75,7 @@ theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts
-/
#print CategoryTheory.Limits.HasFiniteCoproducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite coproducts if there is a chosen colimit for every diagram
with shape `discrete J`, where we have `[fintype J]`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -32,7 +32,7 @@ namespace CategoryTheory.Limits
variable (C : Type u) [Category.{v} C]
#print CategoryTheory.Limits.HasFiniteProducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite products if there is a chosen limit for every diagram
with shape `discrete J`, where we have `[finite J]`.
@@ -75,7 +75,7 @@ theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts
-/
#print CategoryTheory.Limits.HasFiniteCoproducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite coproducts if there is a chosen colimit for every diagram
with shape `discrete J`, where we have `[fintype J]`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -25,7 +25,7 @@ universe w v u
open CategoryTheory
-open Classical
+open scoped Classical
namespace CategoryTheory.Limits
mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c
@@ -32,7 +32,7 @@ namespace CategoryTheory.Limits
variable (C : Type u) [Category.{v} C]
#print CategoryTheory.Limits.HasFiniteProducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite products if there is a chosen limit for every diagram
with shape `discrete J`, where we have `[finite J]`.
@@ -75,7 +75,7 @@ theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts
-/
#print CategoryTheory.Limits.HasFiniteCoproducts /-
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite coproducts if there is a chosen colimit for every diagram
with shape `discrete J`, where we have `[fintype J]`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2
@@ -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 category_theory.limits.shapes.finite_products
-! leanprover-community/mathlib commit ac3ae212f394f508df43e37aa093722fa9b65d31
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! 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.Limits.Shapes.Products
/-!
# Categories with finite (co)products
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Typeclasses representing categories with (co)products over finite indexing types.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -67,7 +67,7 @@ noncomputable example [HasFiniteProducts C] (X : C) : C :=
/-- If a category has all products then in particular it has finite products.
-/
theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts C :=
- ⟨fun n => hasLimitsOfShapeOfEquivalence (Discrete.equivalence Equiv.ulift.{w})⟩
+ ⟨fun n => hasLimitsOfShape_of_equivalence (Discrete.equivalence Equiv.ulift.{w})⟩
#align category_theory.limits.has_finite_products_of_has_products CategoryTheory.Limits.hasFiniteProducts_of_hasProducts
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5
@@ -28,6 +28,7 @@ namespace CategoryTheory.Limits
variable (C : Type u) [Category.{v} C]
+#print CategoryTheory.Limits.HasFiniteProducts /-
/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite products if there is a chosen limit for every diagram
with shape `discrete J`, where we have `[finite J]`.
@@ -38,13 +39,17 @@ We require this condition only for `J = fin n` in the definition, then deduce a
class HasFiniteProducts : Prop where
out (n : ℕ) : HasLimitsOfShape (Discrete (Fin n)) C
#align category_theory.limits.has_finite_products CategoryTheory.Limits.HasFiniteProducts
+-/
+#print CategoryTheory.Limits.hasFiniteProducts_of_hasFiniteLimits /-
/-- If `C` has finite limits then it has finite products. -/
instance (priority := 10) hasFiniteProducts_of_hasFiniteLimits [HasFiniteLimits C] :
HasFiniteProducts C :=
⟨fun n => inferInstance⟩
#align category_theory.limits.has_finite_products_of_has_finite_limits CategoryTheory.Limits.hasFiniteProducts_of_hasFiniteLimits
+-/
+#print CategoryTheory.Limits.hasLimitsOfShape_discrete /-
instance hasLimitsOfShape_discrete [HasFiniteProducts C] (ι : Type w) [Finite ι] :
HasLimitsOfShape (Discrete ι) C :=
by
@@ -52,17 +57,21 @@ instance hasLimitsOfShape_discrete [HasFiniteProducts C] (ι : Type w) [Finite
haveI := has_finite_products.out C n
exact has_limits_of_shape_of_equivalence (discrete.equivalence e.symm)
#align category_theory.limits.has_limits_of_shape_discrete CategoryTheory.Limits.hasLimitsOfShape_discrete
+-/
/-- We can now write this for powers. -/
noncomputable example [HasFiniteProducts C] (X : C) : C :=
∏ fun i : Fin 5 => X
+#print CategoryTheory.Limits.hasFiniteProducts_of_hasProducts /-
/-- If a category has all products then in particular it has finite products.
-/
theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts C :=
⟨fun n => hasLimitsOfShapeOfEquivalence (Discrete.equivalence Equiv.ulift.{w})⟩
#align category_theory.limits.has_finite_products_of_has_products CategoryTheory.Limits.hasFiniteProducts_of_hasProducts
+-/
+#print CategoryTheory.Limits.HasFiniteCoproducts /-
/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite coproducts if there is a chosen colimit for every diagram
with shape `discrete J`, where we have `[fintype J]`.
@@ -73,9 +82,11 @@ We require this condition only for `J = fin n` in the definition, then deduce a
class HasFiniteCoproducts : Prop where
out (n : ℕ) : HasColimitsOfShape (Discrete (Fin n)) C
#align category_theory.limits.has_finite_coproducts CategoryTheory.Limits.HasFiniteCoproducts
+-/
attribute [class] has_finite_coproducts
+#print CategoryTheory.Limits.hasColimitsOfShape_discrete /-
instance hasColimitsOfShape_discrete [HasFiniteCoproducts C] (ι : Type w) [Finite ι] :
HasColimitsOfShape (Discrete ι) C :=
by
@@ -83,18 +94,23 @@ instance hasColimitsOfShape_discrete [HasFiniteCoproducts C] (ι : Type w) [Fini
haveI := has_finite_coproducts.out C n
exact has_colimits_of_shape_of_equivalence (discrete.equivalence e.symm)
#align category_theory.limits.has_colimits_of_shape_discrete CategoryTheory.Limits.hasColimitsOfShape_discrete
+-/
+#print CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits /-
/-- If `C` has finite colimits then it has finite coproducts. -/
instance (priority := 10) hasFiniteCoproducts_of_hasFiniteColimits [HasFiniteColimits C] :
HasFiniteCoproducts C :=
⟨fun J => by infer_instance⟩
#align category_theory.limits.has_finite_coproducts_of_has_finite_colimits CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits
+-/
+#print CategoryTheory.Limits.hasFiniteCoproducts_of_hasCoproducts /-
/-- If a category has all coproducts then in particular it has finite coproducts.
-/
theorem hasFiniteCoproducts_of_hasCoproducts [HasCoproducts.{w} C] : HasFiniteCoproducts C :=
⟨fun J => hasColimitsOfShape_of_equivalence (Discrete.equivalence Equiv.ulift.{w})⟩
#align category_theory.limits.has_finite_coproducts_of_has_coproducts CategoryTheory.Limits.hasFiniteCoproducts_of_hasCoproducts
+-/
end CategoryTheory.Limits
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -60,7 +60,7 @@ noncomputable example [HasFiniteProducts C] (X : C) : C :=
/-- If a category has all products then in particular it has finite products.
-/
theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts C :=
- ⟨fun n => hasLimitsOfShape_of_equivalence (Discrete.equivalence Equiv.ulift.{w})⟩
+ ⟨fun n => hasLimitsOfShapeOfEquivalence (Discrete.equivalence Equiv.ulift.{w})⟩
#align category_theory.limits.has_finite_products_of_has_products CategoryTheory.Limits.hasFiniteProducts_of_hasProducts
/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -40,18 +40,18 @@ class HasFiniteProducts : Prop where
#align category_theory.limits.has_finite_products CategoryTheory.Limits.HasFiniteProducts
/-- If `C` has finite limits then it has finite products. -/
-instance (priority := 10) hasFiniteProductsOfHasFiniteLimits [HasFiniteLimits C] :
+instance (priority := 10) hasFiniteProducts_of_hasFiniteLimits [HasFiniteLimits C] :
HasFiniteProducts C :=
⟨fun n => inferInstance⟩
-#align category_theory.limits.has_finite_products_of_has_finite_limits CategoryTheory.Limits.hasFiniteProductsOfHasFiniteLimits
+#align category_theory.limits.has_finite_products_of_has_finite_limits CategoryTheory.Limits.hasFiniteProducts_of_hasFiniteLimits
-instance hasLimitsOfShapeDiscrete [HasFiniteProducts C] (ι : Type w) [Finite ι] :
+instance hasLimitsOfShape_discrete [HasFiniteProducts C] (ι : Type w) [Finite ι] :
HasLimitsOfShape (Discrete ι) C :=
by
rcases Finite.exists_equiv_fin ι with ⟨n, ⟨e⟩⟩
haveI := has_finite_products.out C n
exact has_limits_of_shape_of_equivalence (discrete.equivalence e.symm)
-#align category_theory.limits.has_limits_of_shape_discrete CategoryTheory.Limits.hasLimitsOfShapeDiscrete
+#align category_theory.limits.has_limits_of_shape_discrete CategoryTheory.Limits.hasLimitsOfShape_discrete
/-- We can now write this for powers. -/
noncomputable example [HasFiniteProducts C] (X : C) : C :=
@@ -59,9 +59,9 @@ noncomputable example [HasFiniteProducts C] (X : C) : C :=
/-- If a category has all products then in particular it has finite products.
-/
-theorem hasFiniteProductsOfHasProducts [HasProducts.{w} C] : HasFiniteProducts C :=
- ⟨fun n => hasLimitsOfShapeOfEquivalence (Discrete.equivalence Equiv.ulift.{w})⟩
-#align category_theory.limits.has_finite_products_of_has_products CategoryTheory.Limits.hasFiniteProductsOfHasProducts
+theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts C :=
+ ⟨fun n => hasLimitsOfShape_of_equivalence (Discrete.equivalence Equiv.ulift.{w})⟩
+#align category_theory.limits.has_finite_products_of_has_products CategoryTheory.Limits.hasFiniteProducts_of_hasProducts
/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
/-- A category has finite coproducts if there is a chosen colimit for every diagram
@@ -76,25 +76,25 @@ class HasFiniteCoproducts : Prop where
attribute [class] has_finite_coproducts
-instance hasColimitsOfShapeDiscrete [HasFiniteCoproducts C] (ι : Type w) [Finite ι] :
+instance hasColimitsOfShape_discrete [HasFiniteCoproducts C] (ι : Type w) [Finite ι] :
HasColimitsOfShape (Discrete ι) C :=
by
rcases Finite.exists_equiv_fin ι with ⟨n, ⟨e⟩⟩
haveI := has_finite_coproducts.out C n
exact has_colimits_of_shape_of_equivalence (discrete.equivalence e.symm)
-#align category_theory.limits.has_colimits_of_shape_discrete CategoryTheory.Limits.hasColimitsOfShapeDiscrete
+#align category_theory.limits.has_colimits_of_shape_discrete CategoryTheory.Limits.hasColimitsOfShape_discrete
/-- If `C` has finite colimits then it has finite coproducts. -/
-instance (priority := 10) hasFiniteCoproductsOfHasFiniteColimits [HasFiniteColimits C] :
+instance (priority := 10) hasFiniteCoproducts_of_hasFiniteColimits [HasFiniteColimits C] :
HasFiniteCoproducts C :=
⟨fun J => by infer_instance⟩
-#align category_theory.limits.has_finite_coproducts_of_has_finite_colimits CategoryTheory.Limits.hasFiniteCoproductsOfHasFiniteColimits
+#align category_theory.limits.has_finite_coproducts_of_has_finite_colimits CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits
/-- If a category has all coproducts then in particular it has finite coproducts.
-/
-theorem hasFiniteCoproductsOfHasCoproducts [HasCoproducts.{w} C] : HasFiniteCoproducts C :=
- ⟨fun J => hasColimitsOfShapeOfEquivalence (Discrete.equivalence Equiv.ulift.{w})⟩
-#align category_theory.limits.has_finite_coproducts_of_has_coproducts CategoryTheory.Limits.hasFiniteCoproductsOfHasCoproducts
+theorem hasFiniteCoproducts_of_hasCoproducts [HasCoproducts.{w} C] : HasFiniteCoproducts C :=
+ ⟨fun J => hasColimitsOfShape_of_equivalence (Discrete.equivalence Equiv.ulift.{w})⟩
+#align category_theory.limits.has_finite_coproducts_of_has_coproducts CategoryTheory.Limits.hasFiniteCoproducts_of_hasCoproducts
end CategoryTheory.Limits
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
open Classical
(#11199)
We remove all but one open Classical
s, instead preferring to use open scoped Classical
. The only real side-effect this led to is moving a couple declarations to use Exists.choose
instead of Classical.choose
.
The first few commits are explicitly labelled regex replaces for ease of review.
@@ -19,7 +19,7 @@ universe w v u
open CategoryTheory
-open Classical
+open scoped Classical
namespace 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.
@@ -29,7 +29,7 @@ variable (C : Type u) [Category.{v} C]
with shape `Discrete J`, where we have `[Finite J]`.
We require this condition only for `J = Fin n` in the definition, then deduce a version for any
-`J : Type _` as a corollary of this definition.
+`J : Type*` as a corollary of this definition.
-/
class HasFiniteProducts : Prop where
/-- `C` has finite products -/
@@ -63,7 +63,7 @@ theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts
with shape `Discrete J`, where we have `[Fintype J]`.
We require this condition only for `J = Fin n` in the definition, then deduce a version for any
-`J : Type _` as a corollary of this definition.
+`J : Type*` as a corollary of this definition.
-/
class HasFiniteCoproducts : Prop where
/-- `C` has all finite coproducts -/
@@ -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
-
-! This file was ported from Lean 3 source module category_theory.limits.shapes.finite_products
-! leanprover-community/mathlib commit ac3ae212f394f508df43e37aa093722fa9b65d31
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
import Mathlib.CategoryTheory.Limits.Shapes.Products
+#align_import category_theory.limits.shapes.finite_products from "leanprover-community/mathlib"@"ac3ae212f394f508df43e37aa093722fa9b65d31"
+
/-!
# Categories with finite (co)products
@@ -28,7 +28,7 @@ namespace CategoryTheory.Limits
variable (C : Type u) [Category.{v} C]
-/-- A category has finite products if there is a chosen limit for every diagram
+/-- A category has finite products if there exists a limit for every diagram
with shape `Discrete J`, where we have `[Finite J]`.
We require this condition only for `J = Fin n` in the definition, then deduce a version for any
@@ -62,7 +62,7 @@ theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts
⟨fun _ => hasLimitsOfShape_of_equivalence (Discrete.equivalence Equiv.ulift.{w})⟩
#align category_theory.limits.has_finite_products_of_has_products CategoryTheory.Limits.hasFiniteProducts_of_hasProducts
-/-- A category has finite coproducts if there is a chosen colimit for every diagram
+/-- A category has finite coproducts if there exists a colimit for every diagram
with shape `Discrete J`, where we have `[Fintype J]`.
We require this condition only for `J = Fin n` in the definition, then deduce a version for any
@@ -49,7 +49,7 @@ instance hasLimitsOfShape_discrete [HasFiniteProducts C] (ι : Type w) [Finite
HasLimitsOfShape (Discrete ι) C := by
rcases Finite.exists_equiv_fin ι with ⟨n, ⟨e⟩⟩
haveI : HasLimitsOfShape (Discrete (Fin n)) C := HasFiniteProducts.out n
- exact hasLimitsOfShapeOfEquivalence (Discrete.equivalence e.symm)
+ exact hasLimitsOfShape_of_equivalence (Discrete.equivalence e.symm)
#align category_theory.limits.has_limits_of_shape_discrete CategoryTheory.Limits.hasLimitsOfShape_discrete
/-- We can now write this for powers. -/
@@ -59,7 +59,7 @@ noncomputable example [HasFiniteProducts C] (X : C) : C :=
/-- If a category has all products then in particular it has finite products.
-/
theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts C :=
- ⟨fun _ => hasLimitsOfShapeOfEquivalence (Discrete.equivalence Equiv.ulift.{w})⟩
+ ⟨fun _ => hasLimitsOfShape_of_equivalence (Discrete.equivalence Equiv.ulift.{w})⟩
#align category_theory.limits.has_finite_products_of_has_products CategoryTheory.Limits.hasFiniteProducts_of_hasProducts
/-- A category has finite coproducts if there is a chosen colimit for every diagram
@@ -32,7 +32,7 @@ variable (C : Type u) [Category.{v} C]
with shape `Discrete J`, where we have `[Finite J]`.
We require this condition only for `J = Fin n` in the definition, then deduce a version for any
-`J : Type*` as a corollary of this definition.
+`J : Type _` as a corollary of this definition.
-/
class HasFiniteProducts : Prop where
/-- `C` has finite products -/
@@ -66,7 +66,7 @@ theorem hasFiniteProducts_of_hasProducts [HasProducts.{w} C] : HasFiniteProducts
with shape `Discrete J`, where we have `[Fintype J]`.
We require this condition only for `J = Fin n` in the definition, then deduce a version for any
-`J : Type*` as a corollary of this definition.
+`J : Type _` as a corollary of this definition.
-/
class HasFiniteCoproducts : Prop where
/-- `C` has all finite coproducts -/
@@ -95,4 +95,3 @@ theorem hasFiniteCoproducts_of_hasCoproducts [HasCoproducts.{w} C] : HasFiniteCo
#align category_theory.limits.has_finite_coproducts_of_has_coproducts CategoryTheory.Limits.hasFiniteCoproducts_of_hasCoproducts
end CategoryTheory.Limits
-
The unported dependencies are