Theorems · Theorem · category theory

CategoryTheory.Limits.PullbackCone.IsLimit.lift_fst_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z}
  {t : CategoryTheory.Limits.PullbackCone f g} (ht : CategoryTheory.Limits.IsLimit t) {W : C} (h : W ⟶ X) (k : W ⟶ Y)
  (w : CategoryTheory.CategoryStruct.comp h f = CategoryTheory.CategoryStruct.comp k g) {Z_1 : C} (h_1 : X ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.PullbackCone.IsLimit.lift ht h k w)
      (CategoryTheory.CategoryStruct.comp t.fst h_1) =
    CategoryTheory.CategoryStruct.comp h h_1

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.Category