Theorems · Theorem · category theory

CategoryTheory.ChosenPullbacksAlong.lift_fst

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {Y Z X : C} {f : Y ⟶ X} {g : Z ⟶ X}
  [inst_1 : CategoryTheory.ChosenPullbacksAlong g] {W : C} (a : W ⟶ Y) (b : W ⟶ Z)
  (h : autoParam (CategoryTheory.CategoryStruct.comp a f = CategoryTheory.CategoryStruct.comp b g) _auto_80✝),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.ChosenPullbacksAlong.lift a b h)
      (CategoryTheory.ChosenPullbacksAlong.fst f g) =
    a

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong

Cited by

4 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlong