{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:40:11Z","timestamp":1760150411487,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,5]],"date-time":"2023-11-05T00:00:00Z","timestamp":1699142400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271258","16002203"],"award-info":[{"award-number":["12271258","16002203"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Nanjing University start-up funding for talent research","award":["12271258","16002203"],"award-info":[{"award-number":["12271258","16002203"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>For a quantale I, the unit interval endowed with a continuous triangular norm, we introduce the canonical, op-canonical and Kleisli extensions of the conical I-semifilter monad to I-Rel. It is proved that the op-canonical extension coincides with the Kleisli extension.<\/jats:p>","DOI":"10.3390\/axioms12111034","type":"journal-article","created":{"date-parts":[[2023,11,5]],"date-time":"2023-11-05T07:35:06Z","timestamp":1699169706000},"page":"1034","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Lax Extensions of Conical I-Semifilter Monads"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6493-1539","authenticated-orcid":false,"given":"Gao","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0614-8984","authenticated-orcid":false,"given":"Shao-Qun","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Intelligence Science and Technology, Nanjing University, Suzhou 215163, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hofmann, D., Seal, G.J., and Tholen, W. 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