Theorems · Theorem · category theory

CategoryTheory.Limits.pullback.map_id

∀ {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.Limits.pullback.map f g f g (CategoryTheory.CategoryStruct.id X) (CategoryTheory.CategoryStruct.id Y)
      (CategoryTheory.CategoryStruct.id Z) ⋯ ⋯ =
    CategoryTheory.CategoryStruct.id (CategoryTheory.Limits.pullback f g)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullback