{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T08:34:25Z","timestamp":1648888465719},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2002,12]]},"abstract":"<jats:p> We show that abstract homotopy theory can be used to define a suitable notion of homotopy equivalence for inverse semigroups. As an application of our theory, we prove a theorem for inverse semigroup homomorphisms which is the exact counterpart of the well-known result in topology which states that every continuous function can be factorized into a homotopy equivalence followed by a fibration. We show that this factorization is isomorphic to the one constructed by Steinberg in his \"Fibration Theorem\", originally proved using a generalization of Tilson's derived category. <\/jats:p>","DOI":"10.1142\/s0218196702001061","type":"journal-article","created":{"date-parts":[[2002,12,20]],"date-time":"2002-12-20T11:13:16Z","timestamp":1040382796000},"page":"755-790","source":"Crossref","is-referenced-by-count":3,"title":["THE HOMOTOPY THEORY OF INVERSE SEMIGROUPS"],"prefix":"10.1142","volume":"12","author":[{"given":"MARK V.","family":"LAWSON","sequence":"first","affiliation":[{"name":"Mathematics Divison, School of Informatics, University of Wales, Bangor, Dean Street, Bangor, Gwynedd LL571UT, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JOSEPH","family":"MATTHEWS","sequence":"additional","affiliation":[{"name":"Mathematics Divison, School of Informatics, University of Wales, Bangor, Dean Street, Bangor, Gwynedd LL571UT, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"TIM","family":"PORTER","sequence":"additional","affiliation":[{"name":"Mathematics Divison, School of Informatics, University of Wales, Bangor, Dean Street, Bangor, Gwynedd LL571UT, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(90)90011-6"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(92)90159-D"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573753"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.0025"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1017\/S001309150002321X"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091599001017"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196702001061","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:56:33Z","timestamp":1565128593000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196702001061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12]]},"references-count":6,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2002,12]]}},"alternative-id":["10.1142\/S0218196702001061"],"URL":"https:\/\/doi.org\/10.1142\/s0218196702001061","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,12]]}}}