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We show that the Cantor-Schr\"oder-Bernstein Theorem for homotopy types, or$\infty$-groupoids holds in the following form: For any two types, if each oneis embedded into the other, then they are equivalent. The argument is developedin the language of homotopy type theory, or Voevodsky's univalent foundations(HoTT/UF), and requires classical logic. It follows that the theorem holds inany boolean $\infty$-topos.

The Cantor-Schr\"oder-Bernstein Theorem for $\infty$-groupoids