Small universes

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

Created on 2022-03-03.
Last modified on 2024-10-09.

module foundation.small-universes where

Imports

open import foundation.universe-levels

open import foundation-core.cartesian-product-types
open import foundation-core.small-types

Idea

A universe 𝒰 is said to be small^¶ with respect to 𝒱 if 𝒰 is a 𝒱-small type and each X : 𝒰 is a 𝒱-small type.

is-small-universe :
  (l l1 : Level) → UU (lsuc l1 ⊔ lsuc l)
is-small-universe l l1 = is-small l (UU l1) × ((X : UU l1) → is-small l X)