From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8358 Path: news.gmane.org!not-for-mail From: Tom Leinster Newsgroups: gmane.science.mathematics.categories Subject: Re: non-unital monads Date: Sun, 19 Oct 2014 22:28:12 +0100 (BST) Message-ID: Reply-To: Tom Leinster NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; format=flowed; charset=US-ASCII X-Trace: ger.gmane.org 1413800042 8120 80.91.229.3 (20 Oct 2014 10:14:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 20 Oct 2014 10:14:02 +0000 (UTC) Cc: categories@mta.ca To: Vladimir Voevodsky Original-X-From: majordomo@mlist.mta.ca Mon Oct 20 12:13:52 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Xg9yE-0000Y1-LY for gsmc-categories@m.gmane.org; Mon, 20 Oct 2014 12:13:46 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:53986) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1Xg9xl-0002tT-IY; Mon, 20 Oct 2014 07:13:17 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Xg9xl-0005eC-6Y for categories-list@mlist.mta.ca; Mon, 20 Oct 2014 07:13:17 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8358 Archived-At: Dear Vladimir, > 1. Given a non-unital monad can it have two different "unitality" structures? No. Write T for the endofunctor, m for the multiplication, and e and e' for the two units. Then e = m(e'T)e = m(Te)e' = e', the first and third equalities by the monad axioms, and the second by naturality of e'. Best wishes, Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]