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Anders Mörtberg: The Category of Iterative Sets in Univalent Foundations

Time: Wed 2023-05-03 10.00 - 12.00

Location: Albano house 1, floor 3, Room U (Kovalevsky)

Participating: Anders Mörtberg, Stockholm University

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When working in HoTT/UF the category of h-sets is traditionally used as a univalent version of the category of sets. One consequence of this is that one gets a 1-type of objects instead of an h-set. This is often what one wants in univalent mathematics, but for some applications it is better to give up univalence in favor of an h-set of objects. There are many constructions of such set universes in HoTT/UF and a particularly elegant one is Gylterud's refinement of Aczel's 1978 universe of sets V which is based on W-types. In the talk I will report on ongoing work with Bonnevier, Gratzer and Gylterud to analyze Gylterud's universe from a category theoretic perspective, with the aim of formalizing models of type theory inside of HoTT/UF.