Theorems · Theorem · category theory

CategoryTheory.Limits.IsLimit.fac

∀ {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), CategoryTheory.CategoryStruct.comp (self.lift s) (t.π.app j) = s.π.app j

The map makes the triangle with the two natural transformations commute

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

67 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category