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The Cantor-Schröder-Bernstein Theorem for ∞-groupoids

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If you have a question about this talk, please contact Todd Waugh Ambridge.

Pradic and Brown (2019) showed that, in constructive set theory, Cantor-Schröder-Bernstein implies excluded middle. Their proof uses the compactness (or searchability or omniscience) of the set ℕ∞ of extended natural numbers.

Conversely, we show that, in Voevodsky’s univalent mathematics, excluded middle implies Cantor-Schröder-Bernstein not only for sets, but also for all homotopy types, or ∞-groupoids.

The talk will aim to be relatively self-contained, briefly explaining the relevant bits of univalent mathematics and other necessary background.

This talk is part of the Lab Lunch series.

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