From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8326 Path: news.gmane.org!not-for-mail From: Jiri Adamek Newsgroups: gmane.science.mathematics.categories Subject: papers on colimits of monads available Date: Wed, 17 Sep 2014 14:59:10 +0200 (CEST) Message-ID: Reply-To: Jiri Adamek NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; format=flowed; charset=US-ASCII X-Trace: ger.gmane.org 1410973609 26928 80.91.229.3 (17 Sep 2014 17:06:49 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 17 Sep 2014 17:06:49 +0000 (UTC) To: categories net Original-X-From: majordomo@mlist.mta.ca Wed Sep 17 19:06:44 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1XUIgm-0000fY-91 for gsmc-categories@m.gmane.org; Wed, 17 Sep 2014 19:06:44 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:39653) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XUIfS-0005Mg-6F; Wed, 17 Sep 2014 14:05:22 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XUIfR-0000ux-8M for categories-list@mlist.mta.ca; Wed, 17 Sep 2014 14:05:21 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8326 Archived-At: I would like to announce two papers available on arxiv: ---------------------- J. Adamek, N. Bowler, P. Levy and S. Milius: Coproducts of Monads on Set (http://arxiv.org/abs/1409.3804) (This is an abstract, extended by proofs in the appendix, of a talk presented at LICS 2012.) A monad M on Set is proved to have a coproduct with every monad in the category Monad(Set) iff M is a submonad of either the terminal monad (constant to 1) or an exception monad (sending X to X+E). Calling such monads trivial, we prove that a coproduct of nontrivial monads exists iff the monads have arbitrarily large joint pre-fixpoints. (A pre-fixpoint of an endofunctor M is an object X such that MX is a subobject of X.) A surprisingly simple formula for coproducts of monads in Set is presented -------------------------- J. Adamek: Colimits of Monads (http://arxiv.org/abs/1409.3805) For "set-like" categories A the category Monad(A) is proved to have coequalizers. It also has a colimit of every diagram such that arbitrarily large joint pre-fixpoints of all the monads exist. This is stronger than the well-known fact that accessible monads admit all colimits. Somewhat surprisingly, the category of monads on Gra does not have coequalizers. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]