{"paper":{"title":"Well-Pointed Coalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.LO","authors_text":"Bloomington, Centre for Mathematics of the University of Coimbra, Germany), IN, Indiana University, Ji\\v{r}\\'i Ad\\'amek (Institut f\\\"ur Theoretische Informatik, Lawrence S Moss (Department of Mathematics, Lurdes Sousa (Polytechnic Institute of Viseu, Portugal), Stefan Milius (Institut f\\\"ur Theoretische Informatik, Technische Universit\\\"at Braunschweig, Technische Universit\\\"ut Braunschweig, USA)","submitted_at":"2013-05-02T20:41:31Z","abstract_excerpt":"For endofunctors of varieties preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. The initial algebra consists of all well-pointed coalgebras that are well-founded in the sense of Osius and Taylor. And initial algebras are precisely the final well-founded coalgebras. Finally, the initial iterative algebra consists of all finite well-pointed coalgebras. Numerous examples are discussed e.g. automata, graphs, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0576","kind":"arxiv","version":3},"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"}