From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2716 Path: news.gmane.org!not-for-mail From: nobody@nowhere.invalid (Unknown) Newsgroups: gmane.science.mathematics.categories Subject: (unknown) Date: Wed, 29 Apr 2009 15:27:28 +0000 (UTC) Message-ID: <37031.6081484363$1241018849@news.gmane.org> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241018848 5453 80.91.229.2 (29 Apr 2009 15:27:28 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:27:28 +0000 (UTC) Original-X-From: rrosebru@mta.ca Tue Jun 1 08:40:09 2004 -0300 Return-path: Original-Lines: 66 Xref: news.gmane.org gmane.science.mathematics.categories:2716 Archived-At: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 01 Jun 2004 08:40:09 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BV7aG-0000eY-00 for categories-list@mta.ca; Tue, 01 Jun 2004 08:37:32 -0300 Mime-Version: 1.0 (Apple Message framework v613) To: categories@mta.ca Message-Id: Content-Type: multipart/alternative; boundary=Apple-Mail-6-367120408 From: Rob Goldblatt Subject: categories: preprint on behavioural covarieties Date: Tue, 1 Jun 2004 12:08:22 +1200 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain;charset=ISO-8859-1;format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 1 A preprint of a paper entitled "A comonadic account of behavioural covarieties of coalgebras" is available for downloading as a pdf file from www.mcs.vuw.ac.nz/~rob Rob Goldblatt ABSTRACT: A class K of coalgebras for an endofunctor T on the category of sets is=20= a behavioural covariety if it is closed under disjoint unions and=20 images of bisimulation relations (hence closed under images and domains=20= of coalgebraic morphisms, including subcoalgebras). K may be thought of=20= as the class of all coalgebras that satisfy some computationally=20 significant property. In any logical system suitable for specifying=20 properties of state-transition systems in the Hennessy-Milner style,=20 each formula will define a class of models that is a behavioural=20 variety. Assume that the forgetful functor on T-coalgebras has a right adjoint,=20= providing for the construction of cofree coalgebras, and let G^T be the=20= comonad arising from this adjunction. Then we show that behavioural=20 covarieties K are (isomorphic to) the Eilenberg-Moore categories of=20 coalgebras for certain comonads G^K naturally associated with G^T.=20 These are called pure subcomonads of G^T, and a categorical=20 characterization of them is given, involving a pullback condition on=20 the naturality squares of a transformation from G^K to G^T. We show that=A0 there is a bijective correspondence between = behavioural=20 covarieties of T-coalgebras and isomorphism classes of pure subcomonads=20= of G^T. =20=