{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T11:41:01Z","timestamp":1784720461554,"version":"3.55.0"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100009024","name":"JST ERATO","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100009024","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,9,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Bisimulation and bisimilarity are fundamental notions in comparing state-based systems. Their extensions to a variety of systems have been actively pursued in recent years, a notable direction being quantitative extensions. In this paper we enhance a categorical framework for such extended (bi)simulation notions. We use coalgebras as system models and fibrations for organizing predicates\u2014following the seminal work by Hermida and Jacobs. Endofunctor liftings are crucial predicate-forming ingredients; the first contribution of this work is to extend several extant lifting techniques from particular fibrations to $\\textbf {CLat}_\\wedge $-fibrations over $\\textbf {Set}$. The second contribution of this work is to introduce endolifting morphisms as a mechanism for comparing predicates between fibrations. We apply these techniques by deriving some known properties of the Hausdorff pseudometric and approximate bisimulation in control theory.<\/jats:p>","DOI":"10.1093\/logcom\/exab051","type":"journal-article","created":{"date-parts":[[2021,9,9]],"date-time":"2021-09-09T12:29:55Z","timestamp":1631190595000},"page":"1526-1559","source":"Crossref","is-referenced-by-count":9,"title":["Fibrational bisimulations and quantitative reasoning: Extended version"],"prefix":"10.1093","volume":"31","author":[{"given":"David","family":"Sprunger","sequence":"first","affiliation":[{"name":"National Institute of Informatics , Tokyo 101-8430, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shin-ya","family":"Katsumata","sequence":"additional","affiliation":[{"name":"National Institute of Informatics , Tokyo 101-8430, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00e9r\u00e9my","family":"Dubut","sequence":"additional","affiliation":[{"name":"National Institute of Informatics , Tokyo 101-8430, Japan and Japanese\u2013French Laboratory for Informatics, CNRS, Tokyo 113-0033, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ichiro","family":"Hasuo","sequence":"additional","affiliation":[{"name":"National Institute of Informatics , Tokyo 101-8430, Japan and The Graduate University for Advanced Studies (SOKENDAI), Kanagawa 240-0193, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,9,10]]},"reference":[{"key":"2023090515053866400_ref1","first-page":"1","article-title":"Abstract and concrete categories: the joy of cats","volume":"17","author":"Adamek","year":"2006","journal-title":"Reprints in Theory and Applications of Categories"},{"key":"2023090515053866400_ref2","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1016\/j.jcss.2014.12.002","article-title":"Moss, and Henning Urbat. 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