From: Venkata Rayudu Posina <posinavrayudu@gmail.com>
To: posina <posina@salk.edu>
Cc: categories <categories@mta.ca>
Subject: Double Dualization: Functions on vs. Figures in
Date: Mon, 27 Oct 2014 10:07:05 +0530 [thread overview]
Message-ID: <E1Xijq0-0003jn-IG@mlist.mta.ca> (raw)
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/ ]
reply other threads:[~2014-10-27 4:37 UTC|newest]
Thread overview: [no followups] expand[flat|nested] mbox.gz Atom feed
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=E1Xijq0-0003jn-IG@mlist.mta.ca \
--to=posinavrayudu@gmail.com \
--cc=categories@mta.ca \
--cc=posina@salk.edu \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).