Theorems · Theorem · category theory

CategoryTheory.IsPullback.exists_lift

∀ {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},
  CategoryTheory.IsPullback fst snd f g →
    ∀ {W : C} (h : W ⟶ X) (k : W ⟶ Y),
      CategoryTheory.CategoryStruct.comp h f = CategoryTheory.CategoryStruct.comp k g →
        ∃ l, CategoryTheory.CategoryStruct.comp l fst = h ∧ CategoryTheory.CategoryStruct.comp l snd = k

Defined in

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

Cited by

5 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category