Theorems · Theorem · category theory

CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
  {F G : CategoryTheory.Functor J C} [inst_2 : CategoryTheory.Limits.HasColimit F]
  [inst_3 : CategoryTheory.Limits.HasColimit G] (t : CategoryTheory.Limits.Cocone G) (w : F ≅ G),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.HasColimit.isoOfNatIso w).hom
      (CategoryTheory.Limits.colimit.desc G t) =
    CategoryTheory.Limits.colimit.desc F ((CategoryTheory.Limits.Cocone.precompose w.hom).obj t)

Defined in

Mathlib.CategoryTheory.Limits.HasLimits

Cited by

9 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitCategoryTheory.Limits.HasColimit