Theorems · Theorem · category theory

CategoryTheory.CountableAB4.of_hasExactColimitsOfShape_nat

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [CategoryTheory.Limits.HasFiniteBiproducts C] [CategoryTheory.Limits.HasFiniteLimits C]
  [inst_4 : CategoryTheory.Limits.HasCountableCoproducts C]
  [CategoryTheory.HasExactColimitsOfShape (CategoryTheory.Discrete ℕ) C], CategoryTheory.CountableAB4 C

Checking exact colimits of shape Discrete ℕ is enough for countable AB4, provided that the category has finite biproducts and finite limits.

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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