From: Paul B Levy <P.B.Levy@cs.bham.ac.uk>
To: categories@mta.ca
Subject: question about monoidal categories
Date: Thu, 7 Feb 2008 20:05:47 +0000 (GMT) [thread overview]
Message-ID: <E1JNDzY-0003pl-Hj@mailserv.mta.ca> (raw)
Let F be a functor from a monoidal category M to a category S.
We are given
beta(p,a) : F(p) --> F(p*a)
natural in p,a in M.
If I tell you that, in addition to naturality, beta is "monoidal", I'm
sure you will immediately guess what I mean by this, viz.
(a) for any p,a,b in M
beta(p,a) ; beta(p*a,b) = beta(p,a*b) ; F(alpha(p,a,b))
(b) for any p in M
beta(p,1) = F(rho(p))
Yet I cannot see any reason for giving the name "monoidality" to (a)-(b).
It doesn't appear to be a monoidal natural transformation in the official
sense. There are no monoidal functors in sight.
Can somebody please justify my usage?
Paul
next reply other threads:[~2008-02-07 20:05 UTC|newest]
Thread overview: 9+ messages / expand[flat|nested] mbox.gz Atom feed top
2008-02-07 20:05 Paul B Levy [this message]
2008-02-07 22:36 Richard Garner
2008-02-07 23:58 Jeff Egger
2008-02-08 8:31 Marco Grandis
2008-02-08 9:51 Sam Staton
2008-02-08 20:03 Richard Garner
2011-04-18 10:37 claudio pisani
2011-04-19 1:40 ` Steve Lack
2011-04-20 9:43 claudio pisani
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