Theorems · Theorem · category theory

CategoryTheory.Limits.WidePullback.lift_base_assoc

∀ {J : Type w} {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {B : C} {objs : J → C}
  (arrows : (j : J) → objs j ⟶ B) [inst_1 : CategoryTheory.Limits.HasWidePullback B objs arrows] {X : C} (f : X ⟶ B)
  (fs : (j : J) → X ⟶ objs j) (w : ∀ (j : J), CategoryTheory.CategoryStruct.comp (fs j) (arrows j) = f) {Z : C}
  (h : B ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.WidePullback.lift f fs w)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.WidePullback.base arrows) h) =
    CategoryTheory.CategoryStruct.comp f h

Defined in

Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasWidePullback