From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9902 Path: news.gmane.org!.POSTED.blaine.gmane.org!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: Nomenclature question Date: Sat, 4 May 2019 09:47:52 +0930 Message-ID: Reply-To: David Roberts Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Injection-Info: blaine.gmane.org; posting-host="blaine.gmane.org:195.159.176.226"; logging-data="29663"; mail-complaints-to="usenet@blaine.gmane.org" To: "categories@mta.ca list" Original-X-From: majordomo@mlist.mta.ca Sat May 04 14:18:53 2019 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.55]) by blaine.gmane.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.89) (envelope-from ) id 1hMtcz-0007Xw-4j for gsmc-categories@m.gmane.org; Sat, 04 May 2019 14:18:53 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:39993) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1hMtdU-00069R-Bt; Sat, 04 May 2019 09:19:24 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1hMtbD-0006C8-OZ for categories-list@mlist.mta.ca; Sat, 04 May 2019 09:17:03 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9902 Archived-At: Hello all, is there a name in the literature for a category C equipped with a product functor #: C x C ---> C satisfying *no* axioms? This is a magma object in Cat, but calling 'magma category' seems at risk of confusion. A name that occurred to me is 'magmoidal category', as a portmanteau of 'magma' and 'monoidal category'. Such a category can be further equipped with diagonals, hence a natural transformation id_C => # \Delta_C, for \Delta_C: C --> C x C. Magmoidal categories with diagonals cropped up as a natural minimal requirements for a particular proof, but it's far from clear that nontrivial and non-degenerate examples exist. David David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]