{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:36:35Z","timestamp":1753889795479,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2015,3,25]],"date-time":"2015-03-25T00:00:00Z","timestamp":1427241600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"name":"Ministry of Education, Science and Technological Development of Republic of Serbia","award":["174026"],"award-info":[{"award-number":["174026"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>An operad (this paper deals with non-symmetric operads)may be conceived as a\npartial algebra with a family of insertion operations, Gerstenhaber's circle-i\nproducts, which satisfy two kinds of associativity, one of them involving\ncommutativity. A Cat-operad is an operad enriched over the category Cat of\nsmall categories, as a 2-category with small hom-categories is a category\nenriched over Cat. The notion of weak Cat-operad is to the notion of Cat-operad\nwhat the notion of bicategory is to the notion of 2-category. The equations of\noperads like associativity of insertions are replaced by isomorphisms in a\ncategory. The goal of this paper is to formulate conditions concerning these\nisomorphisms that ensure coherence, in the sense that all diagrams of canonical\narrows commute. This is the sense in which the notions of monoidal category and\nbicategory are coherent. The coherence proof in the paper is much simplified by\nindexing the insertion operations in a context-independent way, and not in the\nusual manner. This proof, which is in the style of term rewriting, involves an\nargument with normal forms that generalizes what is established with the\ncompleteness proof for the standard presentation of symmetric groups. This\ngeneralization may be of an independent interest, and related to matters other\nthan those studied in this paper. Some of the coherence conditions for weak\nCat-operads lead to the hemiassociahedron, which is a polyhedron related to,\nbut different from, the three-dimensional associahedron and permutohedron.<\/jats:p>","DOI":"10.2168\/lmcs-11(1:10)2015","type":"journal-article","created":{"date-parts":[[2015,5,18]],"date-time":"2015-05-18T07:33:27Z","timestamp":1431934407000},"source":"Crossref","is-referenced-by-count":2,"title":["Weak Cat-Operads"],"prefix":"10.46298","volume":"Volume 11, Issue 1","author":[{"given":"Kosta","family":"DOSEN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zoran","family":"Petric","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2015,3,25]]},"reference":[{"key":"976:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1187\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1187\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:05:39Z","timestamp":1681243539000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1187"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,25]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-11(1:10)2015","relation":{"is-same-as":[{"id-type":"arxiv","id":"1005.4633","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1005.4633","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"arxiv","id":"1706.06788","asserted-by":"subject"},{"id-type":"doi","id":"10.1007\/s10485-019-09569-7","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arxiv.1706.06788","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2015,3,25]]},"article-number":"1187"}}