* omega-completions
@ 2001-06-12 1:42 Steve Lack
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From: Steve Lack @ 2001-06-12 1:42 UTC (permalink / raw)
To: categories
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.
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