* ``cofinite sieves''
@ 1998-06-26 9:03 Steve Lack
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From: Steve Lack @ 1998-06-26 9:03 UTC (permalink / raw)
To: categories
Have any topos-theorists or others come across the following
notion?
Let C be a small category, and c an object of C. If X is an
arbitrary set of arrows with codomain c, then
R_X = { f:b-->c | there is no g:a-->b with fg in X}
clearly gives a sieve on c. Of course if X itself were a sieve
then R_X would be its complement, but I'm not assuming X is a
sieve. Say that a sieve R is _cofinite_ if it is of the form
R_X for a finite set X.
Cofinite sieves are closed under finite intersection and universal
quantification along an arbitrary arrow.
Best wishes,
Steve Lack.
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