Theorems · Theorem · category theory

CategoryTheory.Limits.WeightedCone.IsLimit.fac

∀ {J : Type u} [inst : CategoryTheory.Category.{v, u} J] {C : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} C]
  {W : CategoryTheory.Functor J (Type w)} {F : CategoryTheory.Functor J C} {c : CategoryTheory.Limits.WeightedCone W F}
  (hc : c.IsLimit) {Z : C} (π : ⦃j : J⦄ → W.obj j → (Z ⟶ F.obj j))
  (hπ :
    ∀ ⦃j₁ j₂ : J⦄ (x : W.obj j₁) (f : j₁ ⟶ j₂),
      CategoryTheory.CategoryStruct.comp (π x) (F.map f) = π ((CategoryTheory.ConcreteCategory.hom (W.map f)) x))
  {j : J} (x : W.obj j), CategoryTheory.CategoryStruct.comp (hc.lift π hπ) (c.π x) = π x

Defined in

Mathlib.CategoryTheory.Limits.Weighted.HasWeightedLimit

Cited by

3 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category