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[Merged by Bors] - feat(category_theory/limits): finite products from finite limits #8236

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[Merged by Bors] - feat(category_theory/limits): finite products from finite limits #8236

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test
b-mehta Jul 9, 2021
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b-mehta Jul 9, 2021
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6 changes: 4 additions & 2 deletions src/category_theory/limits/shapes/finite_products.lean
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Expand Up @@ -29,7 +29,8 @@ instance has_limits_of_shape_discrete
by { haveI := @has_finite_products.out C _ _ J (classical.dec_eq _), apply_instance }

/-- If `C` has finite limits then it has finite products. -/
lemma has_finite_products_of_has_finite_limits [has_finite_limits C] : has_finite_products C :=
@[priority 10]
instance has_finite_products_of_has_finite_limits [has_finite_limits C] : has_finite_products C :=
⟨λ J 𝒥₁ 𝒥₂, by { resetI, apply_instance }⟩

/--
Expand All @@ -53,7 +54,8 @@ instance has_colimits_of_shape_discrete
by { haveI := @has_finite_coproducts.out C _ _ J (classical.dec_eq _), apply_instance }

/-- If `C` has finite colimits then it has finite coproducts. -/
lemma has_finite_coproducts_of_has_finite_colimits [has_finite_colimits C] :
@[priority 10]
instance has_finite_coproducts_of_has_finite_colimits [has_finite_colimits C] :
has_finite_coproducts C :=
⟨λ J 𝒥₁ 𝒥₂, by { resetI, apply_instance }⟩

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