Theorems · Theorem · category theory

CategoryTheory.Limits.pullback.comp_diagonal_assoc

∀ {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) {Z_1 : C}
  (h : CategoryTheory.Limits.pullback.diagonalObj g ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp f
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.diagonal g) h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.pullback.diagonal (CategoryTheory.CategoryStruct.comp f g))
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.pullback.map (CategoryTheory.CategoryStruct.comp f g)
          (CategoryTheory.CategoryStruct.comp f g) g g f f (CategoryTheory.CategoryStruct.id Z) ⋯ ⋯)
        h)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Diagonal

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks