From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8356 Path: news.gmane.org!not-for-mail From: Vladimir Voevodsky Newsgroups: gmane.science.mathematics.categories Subject: non-unital monads Date: Sat, 18 Oct 2014 19:02:24 +0100 Message-ID: Reply-To: Vladimir Voevodsky NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Mac OS X Mail 7.3 \(1878.6\)) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1413741592 16725 80.91.229.3 (19 Oct 2014 17:59:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 19 Oct 2014 17:59:52 +0000 (UTC) Cc: "Prof. Vladimir Voevodsky" To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sun Oct 19 19:59:47 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 1Xfule-0004KR-Sv for gsmc-categories@m.gmane.org; Sun, 19 Oct 2014 19:59:47 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:52884) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1Xfuky-00014V-5U; Sun, 19 Oct 2014 14:59:04 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Xfuky-00062U-DQ for categories-list@mlist.mta.ca; Sun, 19 Oct 2014 14:59:04 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8356 Archived-At: Hello, I am trying to find some information about non-unital monads (gadgets = with \mu but without \eta). In particular I am interested in the following two questions: 1. Given a non-unital monad can it have two different "unitality" = structures? 2. Is there a concept of a free non-unital monad? For example, I can = think of the "free" non-unital monad generated by the functor X |-> X^2 on sets = as the monad that sends a set X into the set of "homogeneous" expressions made with = one binary operation s such that there is s(x1,x2) and s(s(x1,x2),s(x3,x4)) but no x1 itself = and no s(x1,s(x2,x3)).=20 But what is the universal characterization of it?=20 Thanks! Vladimir. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]