Theorems · Theorem · category theory

CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_apply

∀ {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] {R : Type u_2}
  [inst_3 : Semiring R] [inst_4 : CategoryTheory.Linear R C] (o : CategoryTheory.HomOrthogonal s) {α β : Type}
  [inst_5 : Finite α] [inst_6 : Finite β] {f : α → ι} {g : β → ι} (a : (⨁ fun a => s (f a)) ⟶ ⨁ fun b => s (g b))
  (i : ι), o.matrixDecompositionLinearEquiv a i = o.matrixDecompositionAddEquiv.toFun a i

Defined in

Mathlib.CategoryTheory.Preadditive.HomOrthogonal

Cited by

0 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasFiniteBiproductsSemiringCategoryTheory.LinearFiniteFinite