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An inductive-recursive universe generic for small families (2202.05529v1)
Published 11 Feb 2022 in cs.LO
Abstract: We show that it is possible to construct a universe in all Grothendieck topoi with injective codes a la Pujet and Tabareau which is nonetheless generic for small families. As a trivial consequence, we show that their observational type theory admits interpretations in Grothendieck topoi suitable for use as internal languages.
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