Theorems · Theorem · category theory

CategoryTheory.preservesColimit_of_isIso_post

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (G : CategoryTheory.Functor C D) {J : Type w} [inst_2 : CategoryTheory.Category.{w', w} J]
  (F : CategoryTheory.Functor J C) [inst_3 : CategoryTheory.Limits.HasColimit F]
  [inst_4 : CategoryTheory.Limits.HasColimit (F.comp G)]
  [CategoryTheory.IsIso (CategoryTheory.Limits.colimit.post F G)], CategoryTheory.Limits.PreservesColimit F G

If the comparison morphism colimit (F ⋙ G) ⟶ G.obj (colimit F) is an isomorphism, then G preserves colimits of F.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Limits

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitCategoryTheory.Limits.HasColimitCategoryTheory.IsIso