From: categories <cat-dist@mta.ca>
To: categories <categories@mta.ca>
Subject: Functor algebras
Date: Wed, 7 Jan 1998 12:59:50 -0400 (AST) [thread overview]
Message-ID: <Pine.OSF.3.90.980107125943.31262E-100000@mailserv.mta.ca> (raw)
Date: Tue, 06 Jan 1998 17:26:17 -0600
From: Uday S Reddy <reddy@cs.uiuc.edu>
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 <A, f:FA->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
next reply other threads:[~1998-01-07 16:59 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
1998-01-07 16:59 categories [this message]
1998-01-08 20:28 categories
1998-01-08 20:29 categories
1998-01-12 18:40 categories
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