Theorems · Theorem · category theory

CategoryTheory.AB4Star.of_AB5Star

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasFiniteBiproducts C] [CategoryTheory.Limits.HasFiniteColimits C]
  [inst_4 : CategoryTheory.Limits.HasCofilteredLimitsOfSize.{w, w, v, u} C]
  [CategoryTheory.AB5StarOfSize.{w, w, v, u} C], CategoryTheory.AB4StarOfSize.{w, v, u} C

A category with finite biproducts and finite limits is AB4 if it is AB5.

Defined in: Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasFiniteBiproducts CategoryTheory.Limits.HasFiniteColimits CategoryTheory.Limits.HasCofilteredLimitsOfSize CategoryTheory.AB5StarOfSize

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.HasFiniteBiproductsstatement and proof · cited by 106
CategoryTheory.Limits.HasFiniteColimitsstatement and proof · cited by 34
CategoryTheory.Limits.HasCofilteredLimitsOfSizestatement and proof · cited by 10
CategoryTheory.AB5StarOfSizestatement and proof · cited by 3
CategoryTheory.Limits.hasProducts_of_finite_and_cofilteredstatement · cited by 2
CategoryTheory.hasExactLimitsOfShape_discrete_of_hasExactLimitsOfShape_finset_discrete_opproof · cited by 2
CategoryTheory.AB4StarOfSizestatement · cited by 2

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