{"paper":{"title":"Filtered Colimit Preserving Functors on Models of a Regular Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Henrik Forssell","submitted_at":"2013-06-28T11:04:23Z","abstract_excerpt":"This note recalls the representation of regular theories T in terms of set-valued functors on models given by Makkai(1990), and explicitly states the representation theorem for the classifying topos Set[T] in terms of filtered colimit preserving functors which can be extrapolated from the results of that paper. That representation of Set[T] is then compared with topological representations in the style of Butz and Moerdijk(1998) by showing that for a certain natural topology on the space of models, preserving filtered colimits is the same thing as being `continuous' in the sense of being an eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6789","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}