Theorems · Theorem · category theory

CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom_assoc

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [inst_1 : CategoryTheory.Category.{v₃, u₃} C]
  {F G : CategoryTheory.Functor J C} {s : CategoryTheory.Limits.Cocone F} {t : CategoryTheory.Limits.Cocone G}
  (P : CategoryTheory.Limits.IsColimit s) (Q : CategoryTheory.Limits.IsColimit t) (w : F ≅ G) (j : J) {Z : C}
  (h : t.pt ⟶ Z),
  CategoryTheory.CategoryStruct.comp (s.ι.app j)
      (CategoryTheory.CategoryStruct.comp (P.coconePointsIsoOfNatIso Q w).hom h) =
    CategoryTheory.CategoryStruct.comp (w.hom.app j) (CategoryTheory.CategoryStruct.comp (t.ι.app j) h)

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category