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Univalent polymorphism

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If you have a question about this talk, please contact Tamara von Glehn.

This talk will be concerned with Hyland’s effective topos. It turns out that this topos is the homotopy category of an interesting path category (a path category is essentially a category of fibrant objects in the sense of Brown in which every object is cofibrant). Within this path category one can identify an interesting subclass of the fibrations: the discrete ones. This subclass contains a universal element, which is, however, not univalent. By passing to a more complicated category, one can obtain a universe for discrete hsets which is univalent. These categories provide weak models of the calculus of constructions plus univalent universes plus resizing (weak in the sense that many equalities hold up only in propositional form).

This talk is part of the Category Theory Seminar series.

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