* Inverse limits in Grothendieck categories
@ 2003-07-15 14:11 Mark Hovey
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From: Mark Hovey @ 2003-07-15 14:11 UTC (permalink / raw)
To: categories
It is pretty well-known that Grothendieck abelian categories have all
small limits. It is perhaps less well known that these inverse limits
do not have to have the same exactness properties as the usual module
inverse limits. For example, the infinite product is left exact, but
not exact, in a general Grothendieck category. Since Grothendieck
categories have enough injectives, one can take the right derived
functors of product and the right derived functors of inverse limit.
Since products are not exact, the inverse limit of a sequence could well
have infinitely many nonzero right derived functors, even if it satisfies
a Mittag-Leffler condition.
Does anyone know if right derived functors of products and inverse limits have
even been studied, either in general Grothendieck categories or in
specific examples?
Thanks,
Mark Hovey
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2003-07-15 14:11 Inverse limits in Grothendieck categories Mark Hovey
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