{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T13:06:48Z","timestamp":1772370408638,"version":"3.50.1"},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2010,8,5]],"date-time":"2010-08-05T00:00:00Z","timestamp":1280966400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Edinburgh Mathematical Society"],"published-print":{"date-parts":[[2010,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce the notion of wide representation of an inverse semigroup and prove that with a suitably defined topology there is a space of germs of such a representation that has the structure of an \u00e9tale groupoid. This gives an elegant description of Paterson's universal groupoid and of the translation groupoid of Skandalis, Tu and Yu. In addition, we characterize the inverse semigroups that arise from groupoids, leading to a precise bijection between the class of \u00e9tale groupoids and the class of complete and infinitely distributive inverse monoids equipped with suitable representations, and we explain the sense in which quantales and localic groupoids carry a generalization of this correspondence.<\/jats:p>","DOI":"10.1017\/s001309150800076x","type":"journal-article","created":{"date-parts":[[2010,8,5]],"date-time":"2010-08-05T12:43:20Z","timestamp":1281012200000},"page":"765-785","source":"Crossref","is-referenced-by-count":10,"title":["\u00c9tale groupoids as germ groupoids and their base extensions"],"prefix":"10.1017","volume":"53","author":[{"given":"Dmitry","family":"Matsnev","sequence":"first","affiliation":[]},{"given":"Pedro","family":"Resende","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2010,8,5]]},"reference":[{"key":"S001309150800076X_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(99)00172-3"},{"key":"S001309150800076X_ref004","doi-asserted-by":"publisher","DOI":"10.1142\/3645"},{"key":"S001309150800076X_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1774-9"},{"key":"S001309150800076X_ref002","volume-title":"Cambridge Studies in Advanced Mathematics","volume":"3","author":"Johnstone","year":"1982"},{"key":"S001309150800076X_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/ulect\/031"},{"key":"S001309150800076X_ref006","volume-title":"Lecture Notes in Mathematics","volume":"793","author":"Renault","year":"1980"},{"key":"S001309150800076X_ref003","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1984.112.141"},{"key":"S001309150800076X_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2006.02.004"},{"key":"S001309150800076X_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/S0040-9383(01)00004-0"}],"container-title":["Proceedings of the Edinburgh Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S001309150800076X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T21:10:27Z","timestamp":1556399427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S001309150800076X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8,5]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,10]]}},"alternative-id":["S001309150800076X"],"URL":"https:\/\/doi.org\/10.1017\/s001309150800076x","relation":{},"ISSN":["0013-0915","1464-3839"],"issn-type":[{"value":"0013-0915","type":"print"},{"value":"1464-3839","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,8,5]]}}}