Theorems · Theorem · category theory

CategoryTheory.Limits.pullback.condition

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z}
  [inst_1 : CategoryTheory.Limits.HasPullback f g],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst f g) f =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.snd f g) g

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

122 results in Mathlib

Foundations

Depth 25 from the axioms, rests on 158 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullback