From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/579 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Re: Functor algebras Date: Thu, 8 Jan 1998 16:28:33 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017052 26349 80.91.229.2 (29 Apr 2009 14:57:32 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:57:32 +0000 (UTC) To: categories Original-X-From: cat-dist Thu Jan 8 16:29:19 1998 Original-Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA22065; Thu, 8 Jan 1998 16:28:34 -0400 (AST) Original-Lines: 34 Xref: news.gmane.org gmane.science.mathematics.categories:579 Archived-At: Date: Wed, 7 Jan 1998 23:06:24 -0500 (EST) From: Ernie Manes > > Date: Tue, 06 Jan 1998 17:26:17 -0600 > From: Uday S Reddy > > Happy New Year, everyone. > > I have been wondering about a little question. Category theory texts > talk about "algebras" for an endofunctor, which are arrows of type FA -> > A, and dually coalgebras A -> GA. I am interested in the symmetric > case, arrows of type FA -> GA for endofunctors F and G. > Have such structures been studied? > > This is only scratching the surface. One can ask for a family of such > arrows for an algebra. One can consider functors F,G: C -> D between > different categories leading to algebras of the form GA> where > A is an object of C, and f an arrow in D, and so on. I am also > interested in the "diagonal" case, arrows of type FAA -> GAA where F and > G are functors C^op x C -> C. (Note that all these structures have a > "natural" notion of homomorphisms.) > > I would appreciate any pointers to the literature. > > Uday Reddy > > Algebras of form FA -> GA were considered in some detail by the Prague school in the 1970s. Email Jiri Adamek for precise references. egm