The Cantor-Schr\"oder-Bernstein Theorem for $\infty$-groupoids
Algebraic Geometry
2020-08-27 v2 Logic
Abstract
We show that the Cantor-Schr\"oder-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.
Cite
@article{arxiv.2002.07079,
title = {The Cantor-Schr\"oder-Bernstein Theorem for $\infty$-groupoids},
author = {Martín Hötzel Escardó},
journal= {arXiv preprint arXiv:2002.07079},
year = {2020}
}