Theorems · Theorem · category theory

CategoryTheory.Limits.preservesColimitsOfShape_of_natIso

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {J : Type w} [inst_2 : CategoryTheory.Category.{w', w} J] {F G : CategoryTheory.Functor C D} (h : F ≅ G)
  [CategoryTheory.Limits.PreservesColimitsOfShape J F], CategoryTheory.Limits.PreservesColimitsOfShape J G

Transfer preservation of colimits of shape along a natural isomorphism in the functor.

Defined in: Mathlib.CategoryTheory.Limits.Preserves.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Category CategoryTheory.Limits.PreservesColimitsOfShape

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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.Isostatement and proof · cited by 3,963
CategoryTheory.Limits.PreservesColimitsOfShapestatement and proof · cited by 222
CategoryTheory.Limits.preservesColimit_of_natIsoproof · cited by 6

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.preservesFiniteColimits_of_natIsoproof · cited by 3
CategoryTheory.Limits.preservesColimits_of_natIsoproof · cited by 2
CategoryTheory.Functor.isCardinalAccessible_of_natIsoproof · cited by 2
CategoryTheory.Limits.preservesColimitsOfShape_iff_of_natIsoproof · cited by 0