Abstract
Abstract: We show that the Cantor–Schröder–Bernstein Theorem for homotopy types, or ∞-groupoids, holds in the following form: For any two types, if each one is embedded into the other, then they are equivalent. The argument is developed in the language of homotopy type theory, or Voevodsky’s univalent foundations (HoTT/UF), and requires classical logic. It follows that the theorem holds in any boolean ∞-topos.
| Original language | English |
|---|---|
| Pages (from-to) | 363-366 |
| Number of pages | 4 |
| Journal | Journal of Homotopy and Related Structures |
| Volume | 16 |
| Issue number | 3 |
| Early online date | 28 Jun 2021 |
| DOIs | |
| Publication status | Published - Sept 2021 |
Keywords
- Cantor–Schröder–Bernstein Theorem
- ∞-groupoid
- Homotopy type theory
- Univalent foundations
- ∞-topos
ASJC Scopus subject areas
- Mathematics(all)
- Computer Science(all)