From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/577 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Functor algebras Date: Wed, 7 Jan 1998 12:59:50 -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 1241017051 26343 80.91.229.2 (29 Apr 2009 14:57:31 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:57:31 +0000 (UTC) To: categories Original-X-From: cat-dist Wed Jan 7 13:06:26 1998 Original-Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id MAA01424; Wed, 7 Jan 1998 12:59:50 -0400 (AST) Original-Lines: 23 Xref: news.gmane.org gmane.science.mathematics.categories:577 Archived-At: 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