This is an archived version pinned as of the submission of my master's thesis.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

Complements of type families

module foundation.complements where
Imports 
open import foundation.dependent-pair-types
open import foundation.universe-levels

open import foundation-core.empty-types
open import foundation-core.function-types

Idea

The complement of a type family B over A consists of the type of points in A at which B x is empty.

complement :
  {l1 l2 : Level} {A : UU l1} (B : A → UU l2) → UU (l1 ⊔ l2)
complement {l1} {l2} {A} B = Σ A (is-empty ∘ B)