2026-08-17T04:02:46Z https://drops.dagstuhl.de/oai

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Terminal Coalgebras for Finitary Functors Adámek, Jiří Milius, Stefan Moss, Lawrence S. terminal coalgebra countable iteration descending chain condition We present a result that implies that an endofunctor on a category has a terminal coalgebra obtainable as a countable limit of its terminal-coalgebra sequence. It holds for finitary endofunctors preserving nonempty binary intersections on locally finitely presentable categories, assuming that the posets of strong quotients and subobjects of every finitely presentable object satisfy the descending chain condition. This allows one to adapt finiteness arguments that were originally advanced by Worrell concerning terminal coalgebras for finitary set functors. Examples include the categories of sets, posets, vector spaces, graphs, and nominal sets. A similar argument is presented for the category of metric spaces (although it is not locally finitely presentable). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jiří Adámek and Stefan Milius and Lawrence S. Moss 2025 Is Part Of LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CALCO.2025.3 urn:nbn:de:0030-drops-235623 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.3 eng https://creativecommons.org/licenses/by/4.0/legalcode