Cartesian product types

Content created by Fredrik Bakke, Egbert Rijke, Jonathan Prieto-Cubides, Julian KG, fernabnor and louismntnu.

Created on 2022-02-04.
Last modified on 2023-09-10.

module foundation-core.cartesian-product-types where
Imports 
open import foundation.dependent-pair-types
open import foundation.universe-levels

Definition

Cartesian products of types are defined as dependent pair types, using a constant type family.

prod : {l1 l2 : Level} (A : UU l1) (B : UU l2) → UU (l1 ⊔ l2)
prod A B = Σ A (λ a → B)

pair' :
  {l1 l2 : Level} {A : UU l1} {B : UU l2} → A → B → prod A B
pair' = pair

infixr 15 _×_
_×_ : {l1 l2 : Level} (A : UU l1) (B : UU l2) → UU (l1 ⊔ l2)
A × B = prod A B

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