Theorems · Theorem · category theory

CategoryTheory.HomOrthogonal.matrixDecomposition_id

∀ {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 : Type} [inst_3 : Finite α] {f : α → ι} (i : ι),
  o.matrixDecomposition (CategoryTheory.CategoryStruct.id (⨁ fun a => s (f a))) i = 1

Defined in

Mathlib.CategoryTheory.Preadditive.HomOrthogonal

Cited by

1 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasFiniteBiproductsFinite