{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T00:54:40Z","timestamp":1776214480168,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Game comonads provide a categorical syntax-free approach to finite model\ntheory, and their Eilenberg-Moore coalgebras typically encode important\ncombinatorial parameters of structures. In this paper, we develop a framework\nwhereby the essential properties of these categories of coalgebras are captured\nin a purely axiomatic fashion. To this end, we introduce arboreal categories,\nwhich have an intrinsic process structure, allowing dynamic notions such as\nbisimulation and back-and-forth games, and resource notions such as number of\nrounds of a game, to be defined. These are related to extensional or \"static\"\nstructures via arboreal covers, which are resource-indexed comonadic\nadjunctions. These ideas are developed in a general, axiomatic setting, and\napplied to relational structures, where the comonadic constructions for\npebbling, Ehrenfeucht-Fra\\\"iss\\'e and modal bisimulation games recently\nintroduced by Abramsky et al. are recovered, showing that many of the\nfundamental notions of finite model theory and descriptive complexity arise\nfrom instances of arboreal covers.<\/jats:p>","DOI":"10.46298\/lmcs-19(3:14)2023","type":"journal-article","created":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T07:45:20Z","timestamp":1691653520000},"source":"Crossref","is-referenced-by-count":2,"title":["Arboreal Categories: An Axiomatic Theory of Resources"],"prefix":"10.46298","volume":"Volume 19, Issue 3","author":[{"given":"Samson","family":"Abramsky","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luca","family":"Reggio","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2023,8,10]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/11717\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/11717\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T07:45:21Z","timestamp":1691653521000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/9839"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,10]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-19(3:14)2023","relation":{"has-preprint":[{"id-type":"arxiv","id":"2102.08109v5","asserted-by":"subject"},{"id-type":"arxiv","id":"2102.08109v4","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2102.08109","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2102.08109","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,10]]},"article-number":"9839"}}