From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5884 Path: news.gmane.org!not-for-mail From: Peter May Newsgroups: gmane.science.mathematics.categories Subject: Re: filtered monads? Date: Sun, 30 May 2010 10:40:23 -0500 Message-ID: References: Reply-To: Peter May NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1275265697 4739 80.91.229.12 (31 May 2010 00:28:17 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 31 May 2010 00:28:17 +0000 (UTC) Original-X-From: categories@mta.ca Mon May 31 02:28:15 2010 connect(): No such file or directory 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 4.69) (envelope-from ) id 1OIsrW-00037G-PD for gsmc-categories@m.gmane.org; Mon, 31 May 2010 02:28:14 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OIsMy-0005Xx-P7 for categories-list@mta.ca; Sun, 30 May 2010 20:56:40 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5884 Archived-At: From my perspective, the original definition of operad was designed to produce a (nonnegatively) filtered monad with the same algbras. That was central to all of the early applications, although I don't think I spelled it out categorically. I did spell it out when using it for calculations. The filtration on the monad C was given by subfunctors F_jC such that the unit Id >--> C factored through F_1C and the product CC >--> C was given by restricted functors F_kCF_jC >--> F_{kj}C. (I also preferred F_0C to be the constant functor at the unit object of the underlying symmmetric monoidal category, but that was negotiable). [For admin and other information see: http://www.mta.ca/~cat-dist/ ]