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Subject: Re: Combining monads
Date: Wed, 14 Jan 1998 19:38:11 -0400 (AST)
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Date: Thu, 15 Jan 1998 09:58:50 +1100
From: Ross Street <street@mpce.mq.edu.au>

>Date: Wed, 14 Jan 1998 16:21:51 +0000 (GMT)
>From: Tom Leinster <T.Leinster@dpmms.cam.ac.uk>
>
>
>Is the pullback of a monadic functor along a monadic functor
>necessarily monadic?

No. And I seem to remember this was one of the main points of the thesis
(under Lawvere) of Michel Thie'baud. The thesis title was "Self-dual
structure-semantics & algebraic categories" (Dalhousie University, Halifax,
Nova Scotia, August 1971). Comonads (= cotriples) in Mod (= Bimod = Prof =
Dist) are the subject. Using these to define "algebraic", Michel obtained
stability under pullback.
--Ross