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From: Marco Grandis <grandis@dima.unige.it>
To: categories@mta.ca
Subject: Re: question about monoidal categories
Date: Fri, 8 Feb 2008 09:31:58 +0100	[thread overview]
Message-ID: <E1JNYOU-0004YU-Ji@mailserv.mta.ca> (raw)

Dear Paul,

Let us forget about the monoidal unit and fix (a).

You define a strict semi? monoidal structure on S letting x*y = x.
Then your pair (F, beta) is a lax monoidal functor M --> S. Your
condition (a) is the hexagon of consistency with alpha, which here
reduces to:

F(p)         =          F(p)
   ||                            |
F(p)                    F(p*a)
   |                             |
F(p*(a*b)   -->   F((p*a)*b)

(a single | stands for a downward beta)

Now, to fix also (b), I guess you should add to S a new object which
is a strict identity for the tensor and work out things.
However, if your problem is only about terminology and you do not
want to use the tensor on S in the sequel (eg to compose F with other
monoidal functors), you might not bother about that.

Best regards

Marco





             reply	other threads:[~2008-02-08  8:31 UTC|newest]

Thread overview: 9+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2008-02-08  8:31 Marco Grandis [this message]
  -- strict thread matches above, loose matches on Subject: below --
2011-04-20  9:43 claudio pisani
2011-04-18 10:37 claudio pisani
2011-04-19  1:40 ` Steve Lack
2008-02-08 20:03 Richard Garner
2008-02-08  9:51 Sam Staton
2008-02-07 23:58 Jeff Egger
2008-02-07 22:36 Richard Garner
2008-02-07 20:05 Paul B Levy

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