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Oct 30, 2009 at 16:28 comment added Reid Barton Part of this is general nonsense about locally presentable categories, such as V-Alg, the category of models of an algebraic theory: in general the category of co-W-objects in V-Alg is the same as Hom^L(W-Alg, V-Alg)--the category of functors which are left adjoints, or equivalently preserve all colimits.
Oct 30, 2009 at 2:47 history edited Charles Rezk CC BY-SA 2.5
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Oct 30, 2009 at 2:33 history edited Charles Rezk CC BY-SA 2.5
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Oct 30, 2009 at 2:21 comment added Peter Arndt Aha, true, they are monads, this also proves the remark that modules over TW-V-monoids form varieties again. But you still have to say that they are representable, or is this automatic somehow? And where did you read off the colimit preservation?
Oct 30, 2009 at 1:56 history answered Charles Rezk CC BY-SA 2.5