Theorems · Theorem · category theory

CategoryTheory.Limits.IsLimit.fac_assoc

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [inst_1 : CategoryTheory.Category.{v₃, u₃} C]
  {F : CategoryTheory.Functor J C} {t : CategoryTheory.Limits.Cone F} (self : CategoryTheory.Limits.IsLimit t)
  (s : CategoryTheory.Limits.Cone F) (j : J) {Z : C} (h : F.obj j ⟶ Z),
  CategoryTheory.CategoryStruct.comp (self.lift s) (CategoryTheory.CategoryStruct.comp (t.π.app j) h) =
    CategoryTheory.CategoryStruct.comp (s.π.app j) h

The map makes the triangle with the two natural transformations commute

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

6 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category