categories: omega-completions

[Steve Lack <stevel@maths.usyd.edu.au>]

I recently noticed the following fact, and wondered
if this was known, and if so, whether there was a 
reference. 

Write w for the first infinite ordinal (pronounced omega, and
thought of as a category). The free completion under w-colimits
of a category K can be described as the category of fractions
[w,K][S^-1], where [w,K] is the functor category, and S consists
of all natural transformations of the form A(phi):A-->Af,
where A:w-->K and f:w-->w are functors, and phi:1_w-->f a 
natural transformation.

Steve Lack.