{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T17:59:16Z","timestamp":1718906356821},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"We introduce monoidal width as a measure of complexity for morphisms in\nmonoidal categories. Inspired by well-known structural width measures for\ngraphs, like tree width and rank width, monoidal width is based on a notion of\nsyntactic decomposition: a monoidal decomposition of a morphism is an\nexpression in the language of monoidal categories, where operations are\nmonoidal products and compositions, that specifies this morphism. Monoidal\nwidth penalises the composition operation along ``big'' objects, while it\nencourages the use of monoidal products. We show that, by choosing the correct\ncategorical algebra for decomposing graphs, we can capture tree width and rank\nwidth. For matrices, monoidal width is related to the rank. These examples\nsuggest monoidal width as a good measure for structural complexity of processes\nmodelled as morphisms in monoidal categories.<\/jats:p>","DOI":"10.46298\/lmcs-19(3:15)2023","type":"journal-article","created":{"date-parts":[[2023,10,9]],"date-time":"2023-10-09T08:51:28Z","timestamp":1696841488000},"source":"Crossref","is-referenced-by-count":1,"title":["Monoidal Width"],"prefix":"10.46298","volume":"Volume 19, Issue 3","author":[{"given":"Elena","family":"Di Lavore","sequence":"first","affiliation":[]},{"given":"Pawe\u0142","family":"Soboci\u0144ski","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2023,9,4]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/lmcs.episciences.org\/12379\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/lmcs.episciences.org\/12379\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,9]],"date-time":"2023-10-09T08:51:29Z","timestamp":1696841489000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/10552"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,4]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-19(3:15)2023","relation":{"has-preprint":[{"id-type":"arxiv","id":"2212.13229v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2212.13229v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2212.13229","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2212.13229","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,4]]}}}