From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8367 Path: news.gmane.org!not-for-mail From: Venkata Rayudu Posina Newsgroups: gmane.science.mathematics.categories Subject: Double Dualization: Functions on vs. Figures in Date: Mon, 27 Oct 2014 10:07:05 +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 1414414601 26787 80.91.229.3 (27 Oct 2014 12:56:41 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 27 Oct 2014 12:56:41 +0000 (UTC) Cc: categories To: posina Original-X-From: majordomo@mlist.mta.ca Mon Oct 27 13:56:36 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 1Xijqd-0003WM-WB for gsmc-categories@m.gmane.org; Mon, 27 Oct 2014 13:56:36 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:36000) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1Xijq1-00008j-08; Mon, 27 Oct 2014 09:55:57 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Xijq0-0003jn-IG for categories-list@mlist.mta.ca; Mon, 27 Oct 2014 09:55:56 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8367 Archived-At: Dear All, The constructs of GENERALIZED POINT (Sets for Mathematics, p. 150) and CONCRETE GENERAL (in the context of Functorial Semantics) are similar: (i) both are encountered in the course of getting to know a given object / graph / category; (ii) both begin with measurements (functions on [the given object] as opposed to figures in; Conceptual Mathematics, pp. 82-83); and (iii) both involve a two-step process i.e. double dualization. In light of these similarities, what exactly is the relation between generalized points A --> V (where A is a set of maps B --> V) and concrete generals A --> V (where A is a category of functors B --> V)? In other words, I'd appreciate any pointers to literature that explicitly brings functorial semantics to bear on physics (e.g. center of mass; Sets for Mathematics, p. 101). On a related note, one can get to know a given B by way of figures in B, instead of the above functions on B. Does the figures-and-incidence (Conceptual Mathematics, pp. 249-253) approach to knowing also involves two steps (like double dualization)? Can we think of modelling, for example, an irreflexive directed graph G as a parallel pair of functions source, target: Arrows --> Dots by way of taking points of map objects 1 --> C (where C is a map object of Dot- or Arrow-shaped figures T --> G in the given graph G; Conceptual Mathematics, p. 150) as analogous to double dualization (albeit in the opposite direction)? Thank you, posina namingthegiven.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]