This is an archived version pinned as of the submission of my master's thesis. An up-to-date version may be found online.

Products of tuples of types

module foundation.products-of-tuples-of-types where

Imports

open import elementary-number-theory.natural-numbers

open import foundation.tuples-of-types
open import foundation.universe-levels

open import univalent-combinatorics.standard-finite-types

Idea

The product of an n-tuple of types is their dependent product.

Definition

Products of `n`-tuples of types

product-tuple-types :
  {l : Level} (n : ℕ) → tuple-types l n → UU l
product-tuple-types n A = (i : Fin n) → A i

The projection maps

pr-product-tuple-types :
  {l : Level} {n : ℕ} (A : tuple-types l n) (i : Fin n) →
  product-tuple-types n A → A i
pr-product-tuple-types A i f = f i