论文标题
Cantor-Schröder-Bernstein定理$ \ infty $ groupoids
The Cantor-Schröder-Bernstein Theorem for $\infty$-groupoids
论文作者
论文摘要
我们表明，Cantor-Schröder-Bernstein定理用于同型类型，或$ \ infty $ groupoids以以下形式保持：对于任何两种类型，如果每种类型都嵌入了另一个类型，则它们是等效的。该论点是用同质类型理论的语言或Voevodsky的单价基础（HOTT/UF）开发的，需要经典的逻辑。因此，该定理在任何布尔$ \ infty $ -TOPOS中都包含。
We show that the Cantor-Schröder-Bernstein Theorem for homotopy types, or $\infty$-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 $\infty$-topos.
