Theorems · Theorem · category theory

CategoryTheory.Limits.pullback.diagonal_comp

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X Y Z : C}
  [inst_1 : CategoryTheory.Limits.HasPullbacks C] (f : X ⟶ Y) (g : Y ⟶ Z),
  CategoryTheory.Limits.pullback.diagonal (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.diagonal f)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullbackDiagonalMapIdIso f f g).inv
        (CategoryTheory.Limits.pullback.snd (CategoryTheory.Limits.pullback.diagonal g)
          (CategoryTheory.Limits.pullback.map (CategoryTheory.CategoryStruct.comp f g)
            (CategoryTheory.CategoryStruct.comp f g) g g f f (CategoryTheory.CategoryStruct.id Z) ⋯ ⋯)))

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Diagonal

Cited by

0 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks