{"paper":{"title":"Terminal Coalgebras and Non-wellfounded Sets in Homotopy Type Theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Elisabeth Stenholm, H{\\aa}kon Robbestad Gylterud, Niccol\\`o Veltri","submitted_at":"2020-01-18T16:16:06Z","abstract_excerpt":"Non-wellfounded material sets have been modelled in Martin-L\\\"of type theory by Lindstr\\\"om using setoids. In this paper we construct models of non-wellfounded material sets in Homotopy Type Theory (HoTT) where equality is interpreted as the identity type. The first model satisfies Scott's Anti-Foundation Axiom (SAFA) and dualises the construction of iterative sets. The second model satisfies Aczel's Anti-Foundation Axiom (AFA), and is constructed by adaption of Aczel--Mendler's terminal coalgebra theorem to type theory, which requires propositional resizing.\n  In an bid to extend coalgebraic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.06696","kind":"arxiv","version":7},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.06696/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}