The Cantor–Schröder–Bernstein Theorem for $$\infty $$-groupoids
| Autor: | Martín Hötzel Escardó |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Computer Science::Machine Learning
Pure mathematics Algebra and Number Theory Functional analysis Homotopy Classical logic Algebraic topology Computer Science::Digital Libraries Topos theory Statistics::Machine Learning Number theory Computer Science::Mathematical Software Homotopy type theory Geometry and Topology Univalent foundations Mathematics |
| Zdroj: | Journal of Homotopy and Related Structures. 16:363-366 |
| ISSN: | 1512-2891 2193-8407 |
| DOI: | 10.1007/s40062-021-00284-6 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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