#
The Frobenius relations meet linear distributivity

##
J.M. Egger

The notion of Frobenius algebra originally arose in ring theory, but
it is a fairly easy observation that this notion can be extended to
arbitrary monoidal categories.
But, is this really the correct level of generalisation?
For example, when studying Frobenius algebras in the *-autonomous
category $\Sup$, the standard concept using only the usual tensor
product is less interesting than a similar one in which both the usual
tensor product and its de Morgan dual (*par*) are used.
Thus we maintain that the notion of linear-distributive category
(which has both a tensor and a par, but is nevertheless more general
than the notion of monoidal category) provides the correct framework
in which to interpret the concept of Frobenius algebra.

Keywords:
Frobenius algebras, linear distributive categories

2000 MSC:
03F52,18D10,18D15

*Theory and Applications of Categories,*
Vol. 24, 2010,
No. 2, pp 25-38.

http://www.tac.mta.ca/tac/volumes/24/2/24-02.dvi

http://www.tac.mta.ca/tac/volumes/24/2/24-02.ps

http://www.tac.mta.ca/tac/volumes/24/2/24-02.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/24/2/24-02.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/24/2/24-02.ps

TAC Home