2026-07-23T17:36:21Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20333 2024-07-05T06:20:34Z ddc:004 open_access

Univalent Enriched Categories and the Enriched Rezk Completion van der Weide, Niels enriched categories univalent categories homotopy type theory univalent foundations Rezk completion Enriched categories are categories whose sets of morphisms are enriched with extra structure. Such categories play a prominent role in the study of higher categories, homotopy theory, and the semantics of programming languages. In this paper, we study univalent enriched categories. We prove that all essentially surjective and fully faithful functors between univalent enriched categories are equivalences, and we show that every enriched category admits a Rezk completion. Finally, we use the Rezk completion for enriched categories to construct univalent enriched Kleisli categories. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Niels van der Weide 2024 Is Part Of LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2024.4 urn:nbn:de:0030-drops-203337 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.4 eng https://creativecommons.org/licenses/by/4.0/legalcode