Theorems · Theorem · category theory

CategoryTheory.Adjunction.hasColimitsOfShape_of_equivalence

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {J : Type u} [inst_2 : CategoryTheory.Category.{v, u} J] (E : CategoryTheory.Functor C D) [E.IsEquivalence]
  [CategoryTheory.Limits.HasColimitsOfShape J D], CategoryTheory.Limits.HasColimitsOfShape J C

Transport a HasColimitsOfShape instance across an equivalence.

Defined in: Mathlib.CategoryTheory.Adjunction.Limits
Cited by: 4 results in Mathlib
Foundations: Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.IsEquivalence CategoryTheory.Limits.HasColimitsOfShape

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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.Functorstatement and proof · cited by 16,252
CategoryTheory.Limits.HasColimitsOfShapestatement and proof · cited by 308
CategoryTheory.Functor.IsEquivalencestatement and proof · cited by 111
CategoryTheory.Adjunction.hasColimit_of_comp_equivalenceproof · cited by 1

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.hasInitial_of_equivalenceproof · cited by 1
CategoryTheory.HasExactColimitsOfShape.of_codomain_equivalencestatement and proof · cited by 1
CategoryTheory.IsGrothendieckAbelian.of_equivalenceproof · cited by 1
CategoryTheory.Adjunction.has_colimits_of_equivalenceproof · cited by 0