English

An inductive-recursive universe generic for small families

Logic in Computer Science 2022-02-14 v1

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.

Cite

@article{arxiv.2202.05529,
  title  = {An inductive-recursive universe generic for small families},
  author = {Daniel Gratzer},
  journal= {arXiv preprint arXiv:2202.05529},
  year   = {2022}
}
R2 v1 2026-06-24T09:31:43.661Z