Theorems · Theorem · category theory

CategoryTheory.HomOrthogonal.matrixDecomposition_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {ι : Type u_1} {s : ι → C}
  [inst_1 : CategoryTheory.Preadditive C] [inst_2 : CategoryTheory.Limits.HasFiniteBiproducts C]
  (o : CategoryTheory.HomOrthogonal s) {α β γ : Type} [inst_3 : Finite α] [inst_4 : Fintype β] [inst_5 : Finite γ]
  {f : α → ι} {g : β → ι} {h : γ → ι} (z : (⨁ fun a => s (f a)) ⟶ ⨁ fun b => s (g b))
  (w : (⨁ fun b => s (g b)) ⟶ ⨁ fun c => s (h c)) (i : ι),
  o.matrixDecomposition (CategoryTheory.CategoryStruct.comp z w) i =
    o.matrixDecomposition w i * o.matrixDecomposition z i

Defined in

Mathlib.CategoryTheory.Preadditive.HomOrthogonal

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasFiniteBiproductsFiniteFintypeFinite