From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/231 Path: news.gmane.org!not-for-mail From: RJ Wood Newsgroups: gmane.science.mathematics.categories Subject: Re: Where does the term monad come from? Date: Mon, 6 Apr 2009 23:06:37 -0300 (ADT) Message-ID: Reply-To: RJ Wood NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1239106643 31471 80.91.229.12 (7 Apr 2009 12:17:23 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 7 Apr 2009 12:17:23 +0000 (UTC) Cc: Rj Wood To: categories@mta.ca Original-X-From: categories@mta.ca Tue Apr 07 14:18:42 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1LrAFq-0007af-Cf for gsmc-categories@m.gmane.org; Tue, 07 Apr 2009 14:18:14 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Lr9Ol-0001OC-46 for categories-list@mta.ca; Tue, 07 Apr 2009 08:23:23 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:231 Archived-At: 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