Small universes

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

Created on 2022-03-03.
Last modified on 2023-06-08.

module foundation.small-universes where
open import foundation.universe-levels

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


A universe UU l1 is said to be small with respect to UU l2 if UU l1 is a UU l2-small type and each X : UU l1 is a UU l2-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)

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