From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7914 Path: news.gmane.org!not-for-mail From: Jiri Adamek Newsgroups: gmane.science.mathematics.categories Subject: preprint "Kan injectivity in order-enriched categories" Date: Mon, 11 Nov 2013 10:10:10 +0100 (CET) Message-ID: Reply-To: Jiri Adamek NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1384208746 5600 80.91.229.3 (11 Nov 2013 22:25:46 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 11 Nov 2013 22:25:46 +0000 (UTC) To: categories net Original-X-From: majordomo@mlist.mta.ca Mon Nov 11 23:25:51 2013 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1VfzvY-0004dw-HC for gsmc-categories@m.gmane.org; Mon, 11 Nov 2013 23:25:48 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:59521) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1Vfztj-0008F2-7n; Mon, 11 Nov 2013 18:23:55 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Vfztj-0006nG-Kp for categories-list@mlist.mta.ca; Mon, 11 Nov 2013 18:23:55 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7914 Archived-At: This is to announce a preprint "Kan Injectivity in Order-Enriched Categories" Jiri Adamek, Lurdes Sousa and Jiri Velebil we have just uploaded to the arxiv http://arxiv.org/abs/1311.1721 In an order-enriched category Escardo introduced Kan-injectivity of an object X w.r.t. to a class H of moprhisms: this means that all left Kan-extensions of morphisms with codomain X along all members of H exist and the corresponding triangles commute. We study the category LInj(H) of all Kan-injective objects and all morphisms preserving left Kan-extensions (introduced by Carvalho and Sousa). Example: for H consisting of all subspace embeddings in the category Top_0 of T_0 spaces LInj(H) is the category of continuous lattices and meet-preserving continuous functions. Every KZ-monadic category has the form LInj(H). Conversely, given a set H of moprhisms in a "reasonable" order-enriched category, then LInj(H) is proved to be KZ-monadic. However, a class of continuous functions in Top_0 is presented for which LInj(H) is not KZ-monadic. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]