Ancestors

Written by Naïm Camille Favier on 2025-01-14 at 19:04

Is there a simple enough condition on a category C for PSh(C) to have split supports (every subterminal object is projective), assuming choice in the metatheory? I think it's enough to ask for the terminal object to be projective, so the question is the same as "which shapes of diagrams have all limits in the category of nonempty sets"?

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Toot

Written by Martin Escardo on 2025-01-14 at 20:30

@ncf

It makes a difference whether you ask this question externally or externally.

I haven't thought about the external question.

But if "every type has split support" is interpreted internally, then every object has decidable equality, including the object of truth values, and hence excluded middle holds (the topos is boolean). Conversely, if the topos is boolean, then every type has split support.

https://lmcs.episciences.org/3217

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Descendants

Written by Naïm Camille Favier on 2025-01-14 at 20:31

@MartinEscardo Yeah I meant externally.

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