monads on model categories

[Andrew Salch <asalch@turing.math.wayne.edu>]

Suppose C is a category and T is a monad on C. One knows that one can
factor T into a composite GF, where F,G are an adjoint pair of functors,
and in fact one knows that there are two universal ways to do this, a
Kleisli/initial construction and an Eilenberg-Moore/terminal construction.

Now suppose C is a model category and T is a monad on C which preserves
weak equivalences. One would like to know that T factors as GF, where F,G
are a Quillen pair. Is this always possible and does one have Kleisli-like
and Eilenberg-Moore-like constructions with appropriate universal
properties? I am sure people have worked on these questions before; where
can I read about this?

Thanks,
Andrew S.


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]