From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8451 Path: news.gmane.org!not-for-mail From: Venkata Rayudu Posina Newsgroups: gmane.science.mathematics.categories Subject: Cohesion and the category of categories Date: Tue, 6 Jan 2015 12:47:41 +0530 Message-ID: Reply-To: Venkata Rayudu Posina NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: ger.gmane.org 1420549634 28156 80.91.229.3 (6 Jan 2015 13:07:14 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 6 Jan 2015 13:07:14 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Tue Jan 06 14:07:08 2015 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 1Y8Tmg-0002r9-8N for gsmc-categories@m.gmane.org; Tue, 06 Jan 2015 14:02:54 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:38216) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1Y8TlR-000887-Se; Tue, 06 Jan 2015 09:01:37 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Y8TlR-0000zt-Gq for categories-list@mlist.mta.ca; Tue, 06 Jan 2015 09:01:37 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8451 Archived-At: Dear All, Since the structure of CATEGORY is of reflexive graph type and since the category of reflexive graphs is cohesive, can we say that the category of categories is cohesive. I am not sure how the additional structure i.e. composition that a category has on top of the reflexive graph structure effects its cohesiveness. I am thinking that somewhat like reversible graphs, which have additional structure (action of involution) besides the reflexive graph structure (action of two idempotents) but nevertheless cohesive, the category of categories is cohesive. On the other hand, in going from actions of two idempotents to actions of one idempotent, the cohesiveness of the category of reflexive graphs changes into contrasting quality type of the category of idempotents. Is there a general statement about how cohesiveness of a structure changes as one adds or removes component structures. Thank you, posina http://namingthegiven.wordpress.com/ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]