Theorems · Theorem · category theory

CategoryTheory.hasExactLimitsOfShape_discrete_of_hasExactLimitsOfShape_finset_discrete_op

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [CategoryTheory.Limits.HasFiniteBiproducts C] [CategoryTheory.Limits.HasFiniteColimits C] (J : Type u_1)
  [inst_4 : CategoryTheory.Limits.HasLimitsOfShape (CategoryTheory.Discrete J) C]
  [inst_5 : CategoryTheory.Limits.HasLimitsOfShape (Finset (CategoryTheory.Discrete J))ᵒᵖ C]
  [CategoryTheory.HasExactLimitsOfShape (Finset (CategoryTheory.Discrete J))ᵒᵖ C],
  CategoryTheory.HasExactLimitsOfShape (CategoryTheory.Discrete J) C

HasExactLimitsOfShape (Finset (Discrete J))ᵒᵖ C implies HasExactLimitsOfShape (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.HasFiniteColimitsCategoryTheory.Limits.HasLimitsOfShapeCategoryTheory.Limits.HasLimitsOfShapeCategoryTheory.HasExactLimitsOfShape