From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9426 Path: news.gmane.org!.POSTED!not-for-mail From: David Yetter Newsgroups: gmane.science.mathematics.categories Subject: Re: How can we have a categorical definition of "theory" Date: Sat, 11 Nov 2017 01:25:14 +0000 Message-ID: Reply-To: David Yetter NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1510440633 21493 195.159.176.226 (11 Nov 2017 22:50:33 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sat, 11 Nov 2017 22:50:33 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Sat Nov 11 23:50:28 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1eDebY-00059C-BM for gsmc-categories@m.gmane.org; Sat, 11 Nov 2017 23:50:24 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:59883) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1eDec9-0000uu-ET; Sat, 11 Nov 2017 18:51:01 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1eDeai-0005ve-BJ for categories-list@mlist.mta.ca; Sat, 11 Nov 2017 18:49:32 -0400 Thread-Index: AQHTWoveGvR/iPATW0iWOnNPxosO8A== Accept-Language: en-US Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9426 Archived-At: In what way is defining a theory dependent on defining a sentence? There are lots of categorical definitions of theories of various sorts: Operads, PROPs, Lawvere theories,..., even monads. One of the points of category theory, esp. higher category theory, has been to liberate mathematical thought from being bound to strings of symbols like terms and sentences. Best Thougths, David Yetter Professor of Mathematics Kansas State University [For admin and other information see: http://www.mta.ca/~cat-dist/ ]