Theorems · Theorem · category theory

CategoryTheory.IsPullback.lift_fst

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P X Y Z : C} {fst : P ⟶ X} {snd : P ⟶ Y} {f : X ⟶ Z}
  {g : Y ⟶ Z} (hP : CategoryTheory.IsPullback fst snd f g) {W : C} (h : W ⟶ X) (k : W ⟶ Y)
  (w : CategoryTheory.CategoryStruct.comp h f = CategoryTheory.CategoryStruct.comp k g),
  CategoryTheory.CategoryStruct.comp (hP.lift h k w) fst = h

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs

Cited by

23 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category