Theorems · Theorem · category theory

CategoryTheory.Limits.weakPullback.lift_fst

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {W X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z}
  [inst_1 : CategoryTheory.Limits.HasWeakPullback f g] (h : W ⟶ X) (k : W ⟶ Y)
  (w : CategoryTheory.CategoryStruct.comp h f = CategoryTheory.CategoryStruct.comp k g),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.weakPullback.lift h k w)
      (CategoryTheory.Limits.weakPullback.fst f g) =
    h

Defined in

Mathlib.CategoryTheory.Limits.WeakLimits.WeakPullbacks

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasWeakPullback