Theorems · Theorem · category theory

CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp_assoc

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
  {F : CategoryTheory.Functor J C} [inst_2 : CategoryTheory.Limits.HasLimit F] {c : CategoryTheory.Limits.Cone F}
  (hc : CategoryTheory.Limits.IsLimit c) (j : J) {Z : C} (h : F.obj j ⟶ Z),
  CategoryTheory.CategoryStruct.comp (hc.conePointUniqueUpToIso (CategoryTheory.Limits.limit.isLimit F)).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.limit.π F j) h) =
    CategoryTheory.CategoryStruct.comp (c.π.app j) h

Defined in

Mathlib.CategoryTheory.Limits.HasLimits

Cited by

4 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimit