Theorems · Theorem · category theory

CategoryTheory.hasExactColimitsOfShape_discrete_of_hasExactColimitsOfShape_finset_discrete

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [CategoryTheory.Limits.HasFiniteBiproducts C] [CategoryTheory.Limits.HasFiniteLimits C] (J : Type u_1)
  [inst_4 : CategoryTheory.Limits.HasColimitsOfShape (CategoryTheory.Discrete J) C]
  [inst_5 : CategoryTheory.Limits.HasColimitsOfShape (Finset (CategoryTheory.Discrete J)) C]
  [CategoryTheory.HasExactColimitsOfShape (Finset (CategoryTheory.Discrete J)) C],
  CategoryTheory.HasExactColimitsOfShape (CategoryTheory.Discrete J) C

HasExactColimitsOfShape (Finset (Discrete J)) C implies HasExactColimitsOfShape (Discrete J) C

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic

Cited by

2 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasFiniteBiproductsCategoryTheory.Limits.HasFiniteLimitsCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.HasExactColimitsOfShape