BOUNCE categories@mta.ca: Approval required: (fwd)

BOUNCE categories@mta.ca: Approval required: (fwd)

[Bob Rosebrugh]

From: Marino Gran <marino.gran@uclouvain.be>
Subject: New Editorial Board of the "Cahiers"
Date: Mon, 15 Dec 2014 21:23:39 +0100
To: categories@mta.ca

Dear Colleagues,

It is a pleasure to announce that the Editorial Board of the "Cahiers de 
Topologie et Geometrie Differentielle Categoriques" will be enlarged and 
modified as follows, starting from January 2015:

Chief Editors: Ehresmann Andree, Gran Marino, Guitart Rene

Editors: Adamek Jiri, Berger Clemens, Bunge Marta, Clementino Maria 
Manuel, Janelidze Zurab, Johnstone Peter, Kock Anders, Lack Stephen, 
Mantovani Sandra, Porter Tim, Pradines Jean, Riehl Emily, Street Ross.

The "Cahiers" were created in 1957 under the initial title "Seminaire 
Ehresmann. Topologie et Geometrie Differentielle", published in the series 
of the "Seminaires de l'Institut Henri Poincare". Starting from Volume II, 
they appeared as an independent publication, the title becoming "Cahiers 
de Topologie et Geometrie Differentielle" in 1966. In 1984 the present 
name "Cahiers de Topologie et Geometrie Differentielle Categoriques" was 
chosen, underlying the continuity with the origin of the journal, and also 
the natural change consisting in placing category theory at the centre of 
the journal. The "Cahiers" is a journal which, since its foundation, is 
under the only responsibility of its Chief-Editor(s). Since 1975, this 
journal has only lived thanks to its subscriptions, without any external 
subvention or material help.

The enlargement of the Editorial Board aims at including a new generation 
of mathematicians and opening the journal to some new research areas where 
category theory is developing and is being applied. The main research 
subject of the journal remains pure category theory, together with its 
applications in topology, differential geometry, algebraic geometry, 
universal algebra, homological algebra, and algebraic topology.

Papers submitted for publication should be sent to one of the editors as a 
pdf file, with a copy to Andree Ehresmann (ehres@u-picardie.fr).

More information on the "Cahiers" can be found on the site

http://ehres.pagesperso-orange.fr/Cahiers/Ctgdc.htm

Correspondence concerning subscriptions and backsets is to be sent to 
Andree Ehresmann by e-mail: ehres@u-picardie.fr

With our best wishes,

Andree Ehresmann, Marino Gran, Rene Guitart


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BOUNCE categories@mta.ca: Approval required: (fwd)

[Bob Rosebrugh]

Date: Wed, 2 Oct 2013 21:57:51 -0300 (ADT)
From: Bob Rosebrugh <rrosebru@mta.ca>
To: categories <categories@mta.ca>
Subject: xy-pic 3.8.9 (fwd)
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed

Following may be of interest to readers of the categories list,

best to all,
Bob Rosebrugh


===============================================================

From the xy-pic mailing list: a new release.

----------------------------------------------------------------------

Message: 1
Date: Tue, 1 Oct 2013 22:26:38 -0400
From: Kristoffer H Rose <krisrose@us.ibm.com>
To: <xy-pic@tug.org>
Subject: [Xy-pic] New release of Xy-pic: 3.8.9



Dear all,

I have released a fresh version of Xy-pic, with a few documentation fixes
and, notably, including Michael's 'diagxy' package as a new module, called
'barr'.  Thanks, Michael, for the permission to do so!

Best regards,
    Kris

__
Kristoffer H Rose, ph.d. <krisrose@us.ibm.com> +1(914)945-2347
IBM T.J.Watson Research Center, PO Box 704, Yorktown Heights, NY 10598


xy-pic mailing list
xy-pic@tug.org
http://tug.org/mailman/listinfo/xy-pic



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BOUNCE categories@mta.ca: Approval required: (fwd)

[Bob Rosebrugh]

Content-Type: text/plain; charset=utf-8; format=flowed; delsp=yes
To: "Marta Bunge" <martabunge@hotmail.com>, categories@mta.ca, "Tom Hirschowitz" <tom.hirschowitz@univ-savoie.fr>
Subject: Re: Publicity
References: <E1UiTcE-000296-Qy@mlist.mta.ca>
Date: Thu, 13 Jun 2013 09:40:34 +0300
MIME-Version: 1.0
Content-Transfer-Encoding: Quoted-Printable
From: "Revence Kalibwani" <revence@1st.ug>
Message-ID: <op.wylt5wui52s4kz@fardeau.ds.co.ug>
In-Reply-To: <E1Umw4g-00036s-IV@mlist.mta.ca>

Speaking as one who hated mathematics consistently in school, and then  =

came to be deeply intrigued by category theory (because I have a  =

probably-pathological obsession with corollaries), I am forced to concur=
   =

with Tom. I=E2=80=99ll never be a professional mathematician, but someth=
ing about  =

basic category theory just sounds so human. Analogies, homologies,  =

similarities, memories =E2=80=A6 these are the things our minds process =
every time  =

we look at a face, and category theory says =E2=80=9CI can help you draw=
  a bunch  =

of squiggly stuff for that.=E2=80=9D What=E2=80=99s not to love?

=CE=A4=CE=B7=CE=BD Tue, 11 Jun 2013 15:40:33 +0300,=CE=BF(=CE=B7) Tom Hi=
rschowitz  =

<tom.hirschowitz@univ-savoie.fr> =CE=AD=CE=B3=CF=81=CE=B1=CF=88=CE=B5:

> Dear Marta,
>
> Thanks very much for your detailed answer.
>
> First, I agree with you that it is wrong to equate category theory wit=
h
> logic and computation. I don't know whose mistake this is, but it
> certainly is one.
>
> However, it seems to me that people may be led to category theory, or
> more generally any interesting subject matter, for bad reasons --- and=

> that this is sometimes good. (*)
>
> Category-land, as Jean B?nabou calls it, may look like a fortress from=

> the outside. So maybe we should be softer towards people trying to mak=
e
> it look attractive and open.
>
> What do you think?
>
> Best wishes,
> Tom
>
> (*) It was John Baez, `making a fool of himself' as usual, who made me=

> think I could enter the fortress back in 2006. I'll probably never be =
as
> fluent as native category theorists, but I nevertheless think my
> research has improved since then.
>
>
>

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BOUNCE categories@mta.ca: Approval required: (fwd)

[Bob Rosebrugh]

Date: Fri, 19 Oct 2012 07:18:05 +0100 (BST)
From: Jocelyn Ireson-Paine <popx@j-paine.org>
To: categories <categories@mta.ca>
Subject: Re: Algorithms arising from category theory
In-Reply-To: <alpine.LRH.2.02.1210170704400.10360@sphinx.mythic-beasts.com>
References: <alpine.LRH.2.02.1210170704400.10360@sphinx.mythic-beasts.com>
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[Note from moderator: some list members received this post without its 
text so it is being resent.]

On Mon, 15 Oct 2012, Mike Stay wrote:

> I'd like to get more computer programmers interested in category
> theory.
>=20
Yes!

> There's the obvious connection to type theory and categorical
> semantics, but programmers are usually far more interested in
> algorithms.
> ...
> Can any readers point me to other algorithms that were discovered by
> turning to category theory or to reports of problems solved by
> realizing they were instances of an abstraction of another solved
> problem?
>=20
In http://tinyurl.com/98ydhkh , "Computational Category Theory", David=20
Rydeheard and Rod Burstall derive an algorithm for unifying terms (in the=
=20
sense used in logic programming), treating it as the construction of=20
coequalisers. (Their original paper, "A Categorical Unification=20
Algorithm", is on the Web, but I can only find copies that are locked up=20
behind a Springer paywall.) There are more recent such algorithms, e.g.=20
http://tinyurl.com/9rqltv6 , "A categorical approach to unification of=20
generalised terms" by Eklund, Gal=E1n, Medina, Ojeda-Aciego and Valverde.

My "Excelsior" spreadsheet-modularisation software, described in=20
http://www.j-paine.org/calco2011/paper.html , "Module Expressions for=20
Modularising Spreadsheets and Sharing Code between Them", was inspired by=
=20
category theory, specifically by Joseph Goguen's sheaf semantics for=20
interacting objects.

Goguen has used colimits and 3/2-colimits to model conceptual blending and =
the=20
interpretation of metaphors: http://cseweb.ucsd.edu/~goguen/pps/taspm.pdf ,=
=20
"Mathematical Models of Cognitive Space and Time".

Michael Healy has used natural transformations and functors as a guide to=
=20
combining neural networks:=20
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=3D10.1.1.32.2635 , "Catego=
ry=20
Theory Applied to Neural Modeling and Graphical Representations".

Michael Healy, Thomas Caudell, and Timothy Goldsmith have proposed that=20
compound concepts could be represented as categorical diagrams, and that=20
concepts could be compared by comparing these diagrams. They say that for s=
ome=20
simple test examples, the results of these comparisons are fairly close to=
=20
human performance, and that this is therefore worth considering as a=20
mathematical model of human concept representation and comparison:=20
http://repository.unm.edu/handle/1928/6724 , "A Model of Human Categorizati=
on=20
and Similarity Based Upon Category Theory".

Ronnie Brown and Tim Porter suggest that higher-dimensional algebra and=20
colimits might be useful for sensoty integration, though they don't develop=
  any=20
algorithms:
http://arxiv.org/PS_cache/math/pdf/0306/0306223v1.pdf , "Category Theory an=
d=20
Higher Dimensional Algebra: potential descriptive tools in neuroscience".

Manfred Liebmann has used multicategories and operads as a guide to designi=
ng=20
parallel numerical algorithms:=20
http://paralleltoolbox.sourceforge.net/categorytheory.pdf , "Category Theor=
y=20
and the Design of Parallel Numerical Algorithms".

There has been a lot of work on merging ontologies by using categorical=20
constructions, usually pushout and colimit. See e.g. Pascal Hitzler, Markus=
=20
Kr=F6tzsch, Marc Ehrig, York Sure in=20
http://knoesis.cs.wright.edu/faculty/pascal/resources/publications/cando05.=
pdf,=20
"What Is Ontology Merging? - A Category-Theoretical Perspective Using Pusho=
uts"=20
and Google "combining ontologies categorically".

I once suggested that, via algebraic-specification languages such as CafeOB=
J,=20
category theory could be used to guide the construction and modularisation =
of=20
large Web sites: http://www.j-paine.org/alg_web_spec.html , "Algebraic Web=
=20
specification".

There's quite a lot of other stuff out there.

I hope these examples fit the spirit of Mike's question. Quite often, it se=
ems=20
that the authors use category theory as a guide, searching it for construct=
ions=20
that they might instantiate as data structures. They then devise algorithms=
  to=20
build these structures. Usually, they do so informally, rather than by form=
ally=20
deriving the algorithm from a categorical definition. Very often, the=20
categorical construction they use is a pushout or colimit. That's the=20
impression I have, anyway. So what they're doing is along the lines suggest=
ed=20
by Goguen in his "A Categorical Manifesto",=20
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=3D10.1.1.13.362 .

By the way, in=20
http://www.j-paine.org/dobbs/why_be_interested_in_categories.html , "What M=
ight=20
Category Theory do for Artificial Intelligence and Cognitive Science?", I=
=20
suggest that these two fields are ripe for the plundering of apparently=20
unrelated concepts that category theory might be able to unify.

> Mike Stay - metaweta@gmail.com
> http://www.cs.auckland.ac.nz/~mike
> http://reperiendi.wordpress.com
>=20
Jocelyn Ireson-Paine
http://www.j-paine.org/index.html

Jocelyn's Cartoons
http://www.j-paine.org/blog/jocelyns_cartoons/
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BOUNCE categories@mta.ca: Approval required: (fwd)

[Bob Rosebrugh]

Approved: tcas
>From rrosebru  Sat Mar  4 22:36:10 2000
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Date: Sat, 04 Mar 2000 18:36:44 -0800
From: Dusko Pavlovic <dusko@kestrel.edu>
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Subject: Re: categories: dom fibration
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> Can anyone explain why the codomain fibration cod: C^\rightarrow -> C,
> which requires pull-backs, gets loads of attention, while the domain
> fibration dom: C^rightarrow -> C, which works for all C, hardly gets a
> look in?  Is the dom fibration really such a poor relation?

heh, the amount of attention is not always proportional to the depth of
the issue. but in this case, i think, there are good reasons for
asymmetry.

the idea of fibred (or indexed) category theory over, say, a base S, is
that each category C is always given together with all categories C^I of
I-indexed families from C, where I are the objects of S. indeed, ordinary
categories are always given with their set indexed versions. we are
tacitly using C^2 to say "product". joining all such indexed versions of C
as the fibres, we get the fibred presentation of C, its "externalization".

but now, the base category S itself should come about as an object of
category theory over S as well. in ordinary category theory, we often
mention the category of sets. the base fibration cod: Ar(S) --> S is the
externalization of S itself as fibred over S. indeed, its fibres, the
slices S/I are the abstract categories of I-indexed families from S. when
S is Set, they are equivalent to S^I; but the latter may not exist for a
general S. the pullbacks in S correspond to reindexing within S. if there
is no reindexing, then S is a poor base for category theory, because it
cannot even reindex itself.

however, even the categories S that cannot reindex themselves, they can
always comprehend themselves (in a formal sense of categorical
psychology). this is expressed by the functor dom: Ar(S)-->S. whether cod
is a fibration or not, there is always the adjunction cod -| ids -| dom:
Ar(S) -->S, which is the categorical form of the comprehension scheme, as
studied by Lawvere and later others, who generalized the adjunction
requirements away, so that the conceptual link with the set theoretical
idea of comprehension got lost...

in any case, if you embed CAT_S--->FIB/S, then cod: Ar(S)-->S is the image
of S itself, while dom: Ar(S)-->S is not in the image of the embedding,
but a derived concept.

-- dusko