Theorems · Theorem · category theory

CategoryTheory.preservesColimitIso_inv_comp_desc

∀ {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.PreservesColimit F G]
  [inst_4 : CategoryTheory.Limits.HasColimit F] (t : CategoryTheory.Limits.Cocone F),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.preservesColimitIso G F).inv
      (G.map (CategoryTheory.Limits.colimit.desc F t)) =
    CategoryTheory.Limits.colimit.desc (F.comp G) (G.mapCocone t)

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Limits

Cited by

1 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesColimitCategoryTheory.Limits.HasColimit