From: grandis@dima.unige.it
To: categories@mta.ca
Subject: Re: horizontal composition
Date: Tue, 31 Jan 2006 13:53:44 +0100 [thread overview]
Message-ID: <1138712024.43df5dd8f133d@webmail.unige.it> (raw)
You can find the strict version of that result in Prop. 1.4 of
- M. Grandis, Homotopical algebra in homotopical categories, Appl. Categ.
Structures 2 (1994), 351-406.
I do not know if it has been written down elsewhere.
For sure, whiskering of natural transformations with functors is used in:
- R. Street, Categorical structures, in: Handbook of Algebra, Vol. 1, 529-577,
North Holland, Amsterdam 1996.
where you can find the notion of a sesqui-category (which does not assume the
"reduced interchange axiom" you are mentioning).
With best regards
M. Grandis
>
> Does anyone know of a reference for the following definition of a
> bicategory? The primitive composites are:
>
> gf for composable 1-cells
> GF for vertically composable 2-cells
> f*G and F*g for horizontally composable pairs of each
>
> with appropriate axioms including (G*f')(g*F)=(g'*F)(G*f), for
> F:f->f':X->Y and G:g->g':Y->Z. The horizontal composite G*F is defined to
> be the common value of the two vertical composites.
>
> -Susan
next reply other threads:[~2006-01-31 12:53 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2006-01-31 12:53 grandis [this message]
-- strict thread matches above, loose matches on Subject: below --
2006-02-02 7:15 Marco Grandis
2006-01-31 19:22 jean benabou
2006-01-27 16:17 Susan Niefield
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