Functoriality of the type of matrices

Content created by Fredrik Bakke, Jonathan Prieto-Cubides and Egbert Rijke.

Created on 2022-03-22.
Last modified on 2024-03-19.

module linear-algebra.functoriality-matrices where
Imports 
open import elementary-number-theory.natural-numbers

open import foundation.universe-levels

open import linear-algebra.functoriality-vectors
open import linear-algebra.matrices

Idea

Any map f : A → B induces a map matrix A m n → matrix B m n.

Definition

module _
  {l1 l2 : Level} {A : UU l1} {B : UU l2} (f : A → B)
  where

  map-matrix : {m n : ℕ} → matrix A m n → matrix B m n
  map-matrix = map-vec (map-vec f)

Binar maps

module _
  {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} {C : UU l3} (f : A → B → C)
  where

  binary-map-matrix :
    {m n : ℕ} → matrix A m n → matrix B m n → matrix C m n
  binary-map-matrix = binary-map-vec (binary-map-vec f)

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