From: "Fred E.J. Linton" <fejlinton@usa.net>
To: <categories@mta.ca>
Subject: Re: "prime" monads?
Date: Thu, 13 Sep 2007 18:50:19 -0400 [thread overview]
Message-ID: <E1IWChE-0004q2-Ho@mailserv.mta.ca> (raw)
Greg Meredith asks,
> ... are there monads such that the only adjoint
> situations giving rise to them are the Kleisli and Eilenberg-Moore
algebras?
NOt even the identity monad on SETS has this property, as it is
the adjunction monad also for the adjoint pair
[underlying pointset]: [topological spaces] --> SETS ,
[discrete topology on]: SETS --> [topological spaces] .
There ARE a few monads for which the Kleisli and E-M categories
"coincide," however, beyond the identity monads. First example
coming to mind is the FreeVectorSpace monad on SETS. I'm sure
other Categories-readers will point out more.
-- Fred
next reply other threads:[~2007-09-13 22:50 UTC|newest]
Thread overview: 8+ messages / expand[flat|nested] mbox.gz Atom feed top
2007-09-13 22:50 Fred E.J. Linton [this message]
-- strict thread matches above, loose matches on Subject: below --
2007-09-17 8:54 Vaughan Pratt
2007-09-16 8:12 Vaughan Pratt
2007-09-15 8:02 Vaughan Pratt
2007-09-15 1:40 Ross Street
2007-09-14 16:30 George Janelidze
2007-09-13 23:06 Greg Meredith
2007-09-12 20:44 Greg Meredith
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