Theorems · Theorem · category theory

CategoryTheory.Limits.hasFiniteColimits_of_hasInitial_and_pushouts

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Limits.HasInitial C]
  [CategoryTheory.Limits.HasPushouts C], CategoryTheory.Limits.HasFiniteColimits C

Defined in: Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
Cited by: 1 results in Mathlib
Foundations: Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasInitial CategoryTheory.Limits.HasPushouts

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Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Limits.HasInitialstatement and proof · cited by 185
CategoryTheory.Limits.HasPushoutsstatement and proof · cited by 172
CategoryTheory.Limits.HasFiniteColimitsstatement · cited by 34
CategoryTheory.Limits.hasFiniteColimits_of_hasCoequalizers_and_finite_coproductsproof · cited by 1

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.createsFiniteColimitsOfCreatesInitialAndPushoutsproof · cited by 0
CategoryTheory.Limits.preservesFiniteColimits_of_preservesInitial_and_pushoutsproof · cited by 0