From: "Meredith Gregory" <lgreg.meredith@gmail.com>
To: categories@mta.ca
Subject: language for infinitary compositions?
Date: Thu, 4 Sep 2008 16:22:34 -0700 [thread overview]
Message-ID: <E1KbYf7-0001yj-KT@mailserv.mta.ca> (raw)
Categorists,
Is there a commonly accepted language for infinitary compositions? Here's
the sort of thing i'm thinking about. There's a purely syntactic
correspondence between a 'braced' notation and an infix notation for
composition. Suppose we have a categorically-friendly notion of composition,
say c. (Meaning the entities c composes can be viewed as morphisms in a
category and c the categorical composition.) Then we can just as easily
write
- f c g -- c is merely making notationally explicit the interpretation of
'o' in f o g -- we're coloring the 'o', as it were
or
- {c| f, g |c} -- we've moved from infix to (not quite) prefix notation
for the composition.
The braced notation, however, is suggestive of a very powerful notational
mechanism, comprehension notation. We could easily imagine a language
allowing expressions of the form
{c| pattern | predicate |c}
which would denote
pattern{subst_1} c pattern{subst_2} c ...
where subst_i is a substition for 'variables' in the pattern of entities
satisfying the predicate. This would allow reasoning over infinitary
compositions by providing an intensional view of their interior structure.
Surely, such a widget has already been invented. Can someone give me a
reference?
Best wishes,
--greg
--
L.G. Meredith
Managing Partner
Biosimilarity LLC
806 55th St NE
Seattle, WA 98105
+1 206.650.3740
http://biosimilarity.blogspot.com
reply other threads:[~2008-09-04 23:22 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=E1KbYf7-0001yj-KT@mailserv.mta.ca \
--to=lgreg.meredith@gmail.com \
--cc=categories@mta.ca \
/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).