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