Dear Finn, The sheaves for a topology can be defined as those presheaves which send certain diagrams to limits. The diagrams in question are determined by the topology. Similarly, the Elienberg-Moore algebras can be seen as the presheaves on the Kleisli category which send certain diagrams to limits. The limits in question, however, are not (usually) those determined by a topology, thus Street and Walters speak of a generalized topology. Regards, Steve Lack. On 11/01/2011, at 1:46 AM, Finn Lawler wrote:
Hello list,
A theorem of Linton says that the Eilenberg--Moore category of a monad is equivalent to the category of presheaves on its Kleisli category that become representable when restricted to the base category (along the canonical inclusion).
In Street and Walters's paper 'Yoneda structures on 2-categories', J. Algebra 50, 1978, proposition 22 generalizes Linton's result. The authors say in the introduction that
it shows that the Eilenberg--Moore algebras for a monad can be regarded as sheaves for a certain generalized topology on the Kleisli category.
Can anyone shed any light on what they mean by a `generalized topology'?
FL
-- Finn Lawler
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