From: RJ Wood <rjwood@mathstat.dal.ca>
To: categories@mta.ca
Cc: Rj Wood <rjwood@mathstat.dal.ca>
Subject: Re: Where does the term monad come from?
Date: Mon, 6 Apr 2009 23:06:37 -0300 (ADT) [thread overview]
Message-ID: <E1Lr9Ol-0001OC-46@mailserv.mta.ca> (raw)
John Baez wrote:
It's pretty much been said, but I'll say it again:
We can generalize the concept of monoid from Set to any monoidal category
and then to any bicategory. A monoid in Cat is then a monad.
Indeed, most people seem to call a "monoid" in a bicategory a "monad".
Best,
jb
John, given the didactic nature of this thread, I think we should be
more precise about what you mean by `a "monoid" in a bicategory'. For
a bicategory B and an object X therein, B(X,X) (together with composition,
1_X, and the inherited constraints of B) i s a monoidal category and a
monad in B is an object X in B together with a monoid in B(X,X).
Rj
next reply other threads:[~2009-04-07 2:06 UTC|newest]
Thread overview: 17+ messages / expand[flat|nested] mbox.gz Atom feed top
2009-04-07 2:06 RJ Wood [this message]
-- strict thread matches above, loose matches on Subject: below --
2009-04-12 1:30 Steve Lack
2009-04-11 15:43 Thorsten Altenkirch
2009-04-07 16:50 Zinovy Diskin
2009-04-07 15:10 jim stasheff
2009-04-07 7:32 Vaughan Pratt
2009-04-06 20:24 John Baez
2009-04-06 4:52 Patrik Eklund
2009-04-03 13:55 burroni
2009-04-03 4:33 Steve Lack
2009-04-03 4:28 Steve Lack
2009-04-02 13:31 jim stasheff
2009-04-01 21:19 burroni
2009-04-01 19:47 Venanzio Capretta
2009-04-01 18:45 Johannes.Huebschmann
2009-04-01 18:13 Michael Barr
2009-04-01 11:24 Thorsten Altenkirch
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