Theorems · Theorem · category theory

CategoryTheory.Limits.preservesColimit_of_reflects_of_preserves

∀ {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] {K : CategoryTheory.Functor J C} {E : Type u₃}
  [ℰ : CategoryTheory.Category.{v₃, u₃} E] (F : CategoryTheory.Functor C D) (G : CategoryTheory.Functor D E)
  [CategoryTheory.Limits.PreservesColimit K (F.comp G)] [CategoryTheory.Limits.ReflectsColimit (K.comp F) G],
  CategoryTheory.Limits.PreservesColimit K F

If F ⋙ G preserves colimits for K, and G reflects colimits for K ⋙ F, then F preserves colimits for K.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Basic

Cited by

2 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesColimitCategoryTheory.Limits.ReflectsColimit