Subject: categories: Re: horizontal composition

From: [email-masked]
Date: Tue, 31 Jan 2006 13:53:44 +0100

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