Theorems · Theorem · category theory

CategoryTheory.Functor.weightedLimObjObj_w_assoc

∀ {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)
  [inst_2 : CategoryTheory.Limits.HasWeightedLimit W F] ⦃j₁ j₂ : J⦄ (x : W.obj j₁) (f : j₁ ⟶ j₂) {Z : C}
  (h : F.obj j₂ ⟶ Z),
  CategoryTheory.CategoryStruct.comp (W.weightedLimObjObjπ F x) (CategoryTheory.CategoryStruct.comp (F.map f) h) =
    CategoryTheory.CategoryStruct.comp (W.weightedLimObjObjπ F ((CategoryTheory.ConcreteCategory.hom (W.map f)) x)) h

Defined in

Mathlib.CategoryTheory.Limits.Weighted.HasWeightedLimit

Cited by

0 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasWeightedLimit