From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4943 Path: news.gmane.org!not-for-mail From: Vincenzo Ciancia Newsgroups: gmane.science.mathematics.categories Subject: Re: preprint announcement Date: Sun, 07 Jun 2009 21:15:11 +0200 Message-ID: Reply-To: Vincenzo Ciancia NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" X-Trace: ger.gmane.org 1244414910 14072 80.91.229.12 (7 Jun 2009 22:48:30 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 7 Jun 2009 22:48:30 +0000 (UTC) To: Panagis Karazeris , categories@mta.ca Original-X-From: categories@mta.ca Mon Jun 08 00:48:27 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MDRAB-0005x0-2L for gsmc-categories@m.gmane.org; Mon, 08 Jun 2009 00:48:27 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MDQbz-0004sl-Sm for categories-list@mta.ca; Sun, 07 Jun 2009 19:13:07 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4943 Archived-At: Il giorno lun, 01/06/2009 alle 16.15 +0300, Panagis Karazeris ha scritto: > Dear all, >=20 > I would like to announce that the following preprint is available as >=20 > http://arxiv.org/abs/0905.4883 >=20 > as well as from my webpage >=20 > www.math.upatras.gr/~pkarazer >=20 > Final Coalgebras in Accessible Categories, > by Panagis Karazeris, Apostolos Matzaris and Jiri Velebil >=20 > Abstract: > We give conditions on a finitary endofunctor of a finitely accessible > category to admit a final coalgebra. Our conditions always apply to the > case of a finitary endofunctor of a locally finitely presentable (l.f.p= .) > category and they bring an explicit construction of the final coalgebra= in > this case. On the other hand, there are interesting examples of final > coalgebras beyond the realm of l.f.p. categories to which our results > apply. We rely on ideas developed by Tom Leinster for the study of > self-similar objects in topology.=20 >=20 > Best regards, > Panagis Karazeris >=20 I do not see the following paper in the references; would it be worth to provide a comparison? http://www.sciencedirect.com/science?_ob=3DArticleURL&_udi=3DB75H1-4G7MXP= F-4&_user=3D144492&_rdoc=3D1&_fmt=3D&_orig=3Dsearch&_sort=3Dd&view=3Dc&_a= cct=3DC000012038&_version=3D1&_urlVersion=3D0&_userid=3D144492&md5=3D5760= 58372d432ade83f476c43b8b466a Terminal sequences for accessible endofunctors=20 James Worrell Abstract: We consider the behaviour of the terminal sequence of an accessible endofunctor T on a locally presentable category K. The preservation of monics by T is sufficient to imply convergence, necessarily to a terminal coalgebra. We can say much more if K is Set, and =CE=BA is =CF=89= . In that case it is well known that we do not necessarily get convergence at =CF=89, however we show that to ensure convergence we don't need to go to= a higher cardinal, just to the next limit ordinal, =CF=89 + =CF=89. For an =CF=89-accessible endofunctor T on Set the construction of the terminal coalgebra can thus be seen as a two stage construction, with each stage being finitary. The first stage obtains the Cauchy completion of the initial T-algebra as the =CF=89-th object in the terminal sequence= A=CF=89. In the second stage this object is pruned to get the final coalgebra A=CF= =89 +=CF=89. We give an example where A=CF=89 is the solution of the correspo= nding domain equation in the category of complete ultra-metric spaces. Thanks Vincenzo [For admin and other information see: http://www.mta.ca/~cat-dist/ ]