Date: Sun, 29 Jun 1997 11:40:10 -0300 (ADT)
Subject: Query
Date: Thu, 26 Jun 1997 13:57:18 +0300 (IDT)
From: ZIPPIE Gonczarowski <zippie@actcom.co.il>
Dear Colleagues,
I am applying tools of category theory to research in artificial
perception and cognition. A basic category is proposed where every
perception is an object and morphisms capture the flow between
perceptions. Natural transformations capture paths to more cognitive
perceptions.
An Anonymous referee remarked that my category is `very closely related
to comma categories'.
Can anybody refer me to written material that introduces comma categories?
Also, please let me know if you are aware of other research that applies
categorical tools to research in artificial perception and cognition.
Thanks
Zippie
e-mail zippie@actcom.co.il
Dr. Zippora Arzi-Gonczarowski
Typographics, Ltd.
46 Hehalutz St.
Jerusalem 96222, Israel
Date: Mon, 30 Jun 1997 23:39:58 -0300 (ADT)
Subject: Re: Query
Date: Sun, 29 Jun 1997 11:58:50 -0700 (PDT)
From: Dr. Farogh Dovlatshahi <frank@primenet.com>
This is not an answer to your question. But your posting prompts me to
ask a question in the semantics underlying applications of cateogories.
What is the underlying metaphysics of perception (event, processes,
relations ?). How do you capture 'time'. It seems to me the dynamism is in
the arrows -- and there perhaps is where time comes in.
It has always seemed to me that the applications of Cat. The. (for
example in the study of Dynamical Systems) has served as a language to
talk about mathematical, computatianal and procedural complexities ONCE
THESE ARE ALREADY IN PALCE. Cat. is not to replace them as an alternative.
Dr. Farogh Dovlatshahi
>
>
>
> Dear Colleagues,
>
> I am applying tools of category theory to research in artificial
> perception and cognition. A basic category is proposed where every
> perception is an object and morphisms capture the flow between
> perceptions. Natural transformations capture paths to more cognitive
> perceptions.
> An Anonymous referee remarked that my category is `very closely related
> to comma categories'.
>
> Can anybody refer me to written material that introduces comma categories?
> Also, please let me know if you are aware of other research that applies
> categorical tools to research in artificial perception and cognition.
>
> Thanks
>
> Zippie
>
> e-mail zippie@actcom.co.il
>
> Dr. Zippora Arzi-Gonczarowski
> Typographics, Ltd.
> 46 Hehalutz St.
> Jerusalem 96222, Israel
Date: Mon, 30 Jun 1997 23:41:52 -0300 (ADT)
Subject: Re: Query
Date: Sun, 29 Jun 1997 20:49:19 -0400
From: Michael Barr <barr@triples.math.mcgill.ca>
Not that I am blowing my own horn (but why not), you will find something
about comma categories in Barr & Wells, Category Theory for Computing
Science. But no, I know of no other research along those lines.
Michael Barr
Date: Tue, 1 Jul 1997 15:15:39 -0300 (ADT)
Subject: Re: Query
Date: Tue, 1 Jul 1997 09:49:21 -0700
From: Michael J. Healy 206-865-3123 <mjhealy@redwood.rt.cs.boeing.com>
Since there have been some replies to the query about artificial perception,
I suppose it's OK to mention my own work in progress. I have been doing
research in the formal semantics of neural networks. I am working on a
mathematical model in which concepts (formulas) are formed in memory as
colimits. The diagrams involve neural structures representing other
concepts, going all the way back to simple percepts. A concept is stored
in memory as a neuron or neuron pool together with its attendant synaptic
connections. Logically closed portions of memory are theories. Functors
and natural transformations enter in in the usual fashion of categorical
model theory.
There is still a lot of work to do on this, and I am still learning the
mathematics. I do have a proposed neural implementation of it, and am
working on a paper. Previous work along these lines has involved geometric
logic, so that I could understand some of the basics of learning, which for
me involves working with an observational logic. I have a paper on this,
too. Finding reviewers for this kind of material in the neural network
community has been difficult. If any of this sounds interesting enough
to discuss, I certainly wouldn't mind getting some feedback from category
theorists.
Sincerely,
Mike Healy
--
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e
Michael J. Healy A
FA ----------> GA
(425)865-3123 | |
FAX(425)865-2964 | |
Ff | | Gf
c/o The Boeing Company | |
PO Box 3707 MS 7L-66 \|/ \|/
Seattle, WA 98124-2207 ' '
USA FB ----------> GB
e "I'm a natural man."
michael.j.healy@boeing.com B
-or- mjhealy@u.washington.edu
============================================================================
Date: Tue, 1 Jul 1997 15:14:21 -0300 (ADT)
Subject: Re: comma categories
Date: Tue, 1 Jul 1997 11:38:17 -0400
From: Michael Barr <barr@triples.math.mcgill.ca>
You are right. It is called slice categories.
Michael Barr
From: "John G. Stell" <john@cs.keele.ac.uk>
Date: Tue, 1 Jul 1997 09:14:56 +0100
To: barr@triples.math.mcgill.ca
Subject: comma categories
> Not that I am blowing my own horn (but why not), you will find something
> about comma categories in Barr & Wells, Category Theory for Computing
> Science. But no, I know of no other research along those lines.
>
> Michael Barr
Pehaps it would be helpful to the original enquirer to say where
it can be found. I am unable to find it in the index of either edition.
John Stell