Re: Function composition of natural transformations?

[Ronnie Brown <mas010@bangor.ac.uk>]

It may be useful to recall the Ehresmann method of setting up the
exponential law for categories using the double categoy of commuting
squares in a category. This is also written up in

 (R.Brown,  P. NICKOLAS), ``Exponential laws for topological
categories,  groupoids and groups and mapping spaces of
colimits'', {\em Cah. Top. G\'eom.  Diff.} 20 (1979) 179-198.

The nice point is that the category structure is induced by a double
category composition, and so if you have extra structure, such as a
topology, that carries over.

Ronnie Brown




On Tue, 3 Jun 2003, Toby Bartels wrote:

> Steve Vickers wrote:
>
> >It is also possible to use a 2-dimensional syntax, in which horizontal
> >composition is composed horizontally and vertical composition is
> >composed vertically. Then algebraic manipulations are a bit like sliding
> >tiles around in a tray.
>
> Of course this can be done using big diagrams.
> But is there a tight syntax for this just using text?
> Can you point to an example? (preferably a TeX source online,
> but a printed page in a regular journal would also work).
>
>
> -- Toby
>
>
>

Prof R. Brown,
School of Informatics, Mathematics Division,
University of Wales, Bangor
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Gwynedd LL57 1UT, United Kingdom
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(Links to survey articles:
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