gmane.science.mathematics.categories

PhD positions in bialgebraic semantics in Warsaw

Bartek Klin — 2013-05-22T22:01:25

Two PhD student positions will soon be available to work under the direction
of Bartek Klin in the Institute of Informatics, University of Warsaw.

The positions are in the field of semantics of programming
languages and process algebras, in connection to the project
"Modular operational semantics: a bialgebraic approach", funded
by the Polish National Science Center. The applicants should have
solid background in Mathematics and Computer Science, and
be interested in topics such as semantics of programming languages,
category theory, process algebra, formal methods.

The positions will be available from October 2013. Interested
candidates should apply for a PhD fellowship at the Warsaw Center
of Mathematics and Computer Science (http://www.wcmcs.edu.pl/node/38),
with the deadline of

*** June 7th, 2013 ***.

A successful candidate will earn 5000PLN(~1200EUR)/month
(3500PLN tax-free from the WCMCS fellowship + 1500PLN pre-tax funded
by the research project), subject to yearly evaluation of progress.
The posi

Post-doctoral Position at the University of Cambridge

Pierre Clairambault — 2013-05-22T10:45:51

A post-doctoral position is available at the University of Cambridge
Computer Laboratory on the European Research Council Advanced Grant
ECSYM (Events, Causality and Symmetry---the next generation semantics).
The position is initially for one year, starting after 1 July 2013, with
the possibility of renewal after that period. The position is for a
talented researcher in theoretical computer science or mathematics, with
expertise in several of the areas of games and logic, concurrency,
category theory, type theory and semantics.

Further details on the ECSYM project can be found at
http://www.cl.cam.ac.uk/~cdt25/ecsym/

Details on how to apply can be found on
http://www.jobs.cam.ac.uk/job/-28982/

Application deadline: June 16, 2013


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samson< at >60, 28-30 May 2013 Full Program

Bob Coecke — 2013-05-22T11:18:28

A Conference in Honour of Samson Abramsky on the event of his 60th Birthday

28-30 May 2013

Oxford Department of Computer Science, Lecture Theatre B 

Organisers: Bob Coecke, Luke Ong, Prakash Panangaden
Local organisers: Destiny Chen, Aleks Kissinger  

Please contact Destiny Chen <destiny.chen< at >cs.ox.ac.uk> for all questions.

www: http://www.cs.ox.ac.uk/sa60/index.html

PROGRAM:

Tuesday 28th May »

08.30-09.15 Registration and Payment
09.30-10.00 Introduction/welcome by Head of Department
10.00-10.30 Luke Ong
10.30-11.00 Radha Jagadeesan
             Title:  Linearizability, Revisited.
 
11.00-11.30 BREAK
 
11.30-12.00 Nikos Tzevelokos & Andrzej Murawski
             Title: Towards Nominal Abramsky
12.00-12.30 Paul-Andre Mellies
             Title: Dialogue categories and Frobenius
 
12.30-14.00 LUNCH
 
14.00-14.30 Glynn Winskel
             Title: Quantum event structures and strategies''
14.30-15.00 Marcelo Fiore
             Title: The Algebra of DAGs
 
15.00-15.30 BREAK
 
15.30-16.00 Dusko Pavlovic

Call for Papers- special issue APAL

Maria Emilia Maietti — 2013-05-18T08:35:18


-------------------------------------------------------------------------
Call for Papers: Fourth Workshop on Formal Topology (4WFTop)
-------------------------------------------------------------------------
Special Issue of Annals of Pure and Applied Logic
-------------------------------------------------------------------------

The Fourth Workshop on Formal Topology was held in Ljubljana in June 2012:

http://4wft.fmf.uni-lj.si/

The proceedings of this workshop will be published as a special issue of
the Annals of Pure and Applied Logic, with the following guest editors:

Thierry Coquand, Maria Emilia Maietti, Giovanni Sambin, Peter Schuster.

These proceedings are open for high-level research papers on topics from
or closely related to formal topology, that is, constructive and/or
point-free topology including its applications and its foundations.

-------------------------------------------------------------------------
Submissions by email to: 4WFTop.apal< at >math.unipd.it
-----------------------------

Re: separable locale

Michael Fourman — 2013-05-17T12:35:41

Thomas,

Peter is correct about my intention. More precisely, 'separable' is defined in
Formal Spaces (FS) (Fourman & Grayson, Brouwer Centenary Symposium) 3.12(c)
--- although I now find this account unnecessarily obscure.

What you say below is correct classically; constructively there is some subtlety.

A locale is separable iff it is presented (as in FS 1.1) by a countable language
with decidable \leq and countably many *inhabited* basic covers.


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CT2013 - early bird registration

Richard Garner — 2013-05-16T09:46:08

Dear all,

This is a reminder that early bird registration for Category Theory 2013
closes TOMORROW, Friday 17th May. After that, the cost of registration goes
up by 10% across the board.

Any registrations submitted by fax, post or other means at a time
verifiably before the 18th in your local timezone will be deemed eligible
for the early bird rates; any submitted thereafter will not.

The registration page may be found at:

http://web.science.mq.edu.au/groups/coact/seminar/ct2013/registration.html

If you believe you have submitted a registration form already, but have
received no confirmation of its receipt, please email me to let me know.

Richard Garner (for the CT2013 organising committee)

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Re: on a subcategory of algebras for a monad

F. William Lawvere — 2013-05-14T15:49:31

Hi, Emily and Fred
This definition of finiteness can be extended to a definition of smallness.
Double dualisation and coadequacy monads have a big overlap,related to
the Isbell conjugacy between Csheaves and Calgebras where  C is a given
category. Instead of taking C to consist only of 2 and 3 element sets,as in the 
Stone case, let C be a full category of countable sets and ask if C is coadequate
among all sets. Then the fixed algebras for the resulting monad are small in the 
sense of being smaller than the UlamTarski number. That they are sufficiently big 
for all reasonable constructions of geometry and analysis concentrates in the fact
that they are closed under the formation of Hurewicz exponentials, ie that their
  category is Cartesian closed, indeed a topos (the subobject classifier is tautological
since it is in C). It would be desirable to have a general proof of this fact.
         The intuitions connected with historical cases of Mcompleteness require that. 
M is already idempotent, ie does not

GlynnFest Workshop, May 31st and June 1st, Cambridge University Computer Laboratory

2013-05-14T09:27:38

We are happy to announce a workshop to honour Glynn Winskel on the occasion  of his 60th birthday.

The workshop will take place at Cambridge University Computer Laboratory on  May 31st and June 1st.

The speakers will be:

- Samson Abramsky, University of Oxford
- Henrik R. Andersen, Configit
- Steve Brookes, Carnegie-Mellon University
- Pierre-Louis Curien, University of Paris 7
- Olivier Danvy, University of Aarhus
- Marcelo Fiore, University of Cambridge
- Thomas T. Hildebrandt, IT University of Copenhagen
- Martin Hyland, University of Cambridge
- Kim G. Larsen, University of Aalborg
- Ugo Montanari, University of Pisa
- Mogens Nielsen, University of Aarhus
- Prakash Panangaden, McGill University
- Andy Pitts, University of Cambridge
- Gordon Plotkin, University of Edinburgh
- Vladimiro Sassone, University of Southampton

Participation to the workshop is open, but attendees are kindly requested to register in advance.
More details about the workshop venue and program and about the registration procedure

Re: on a subcategory of algebras for a monad

Fred E.J. Linton — 2013-05-13T08:15:15

Hi, Emily,

Another example of interesting classes of "objects those X in C such 
that the unit X -> MX is an isomorphism" (C a pleasant category, M a 
(perhaps familiar) monoid on C):

As C, use the category either of vector spaces, or of Banach spaces 
(if the latter, use linear maps of bound not exceeding 1); and as M 
use the corresponding double-dualization monoid. 

Then: among vector spaces, it's the finite-dimensional ones for which 
the unit is an isomorphism; among Banach spaces, it's the reflexive ones.

So again, behavior with respect to limits is, in either case, not 
(TTBOMK) as you[r grad student] might wish.

Cheers, -- Fred

------ Original Message ------
Received: Sun, 12 May 2013 06:48:45 PM EDT
From: "Fred E.J. Linton" <fejlinton< at >usa.net>
To: Emily Riehl <eriehl< at >math.harvard.edu>, <categories< at >mta.ca>
Subject: categories: Re: on a subcategory of algebras for a monad

the
isomorphism"
I
to
Comp_M
Alg_M
MX
computed
yes,
idempotent




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Zig Zags?

2013-05-13T12:50:57

Dear Toby,

Thank you for your explanations. I really admire your elegant idea to use zig zags instead of 2-pullbacks. 
But I am an old fashioned mathematician and I like precise definitions with which I can (try to) prove precise results.
You suggest to use zig zags. Could you please tell me what are the maps in the zig zags: anafunctors? functors? (in both cases what properties do you assume about them?), equivalences of categories? (in that case in what sense?)
How do you compose your zig zags? You say "directly", do you mean by mere concatenation?
Obviously there would be a huge amount of such zig zags, thus you would probably want to work up to some identification. Could you please tell me, with precision, when two such zig zags between two categories A and B should be identified?
In the case of spans, using 2-pullbacks, what are the maps in your spans, when should two such spans between A and B be identified?
You say, I quote you:

Indeed, so one must also define natural isomorphism of equivalences
If

Re: (In)accessible comonads and (non)Grothendieck toposes

Prof. Peter Johnstone — 2013-05-11T15:26:52

A particular case of this is in SGA4, IV 9.5.4, where it is shown
that the category obtained by (Artin) glueing along a finite-limit-
preserving functor between Grothendieck toposes is a Grothendieck
topos iff the functor is accessible. It was Gavin Wraith, in JPAA 4
(1974), who first observed that Artin glueing is a particular case
of forming a category of coalgebras (and therefore works for
elementary toposes without the accessibility condition).

Peter Johnstone

On Thu, 9 May 2013, David Roberts wrote:



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Re: on a subcategory of algebras for a monad

Fred E.J. Linton — 2013-05-11T05:09:32

Hi, Emily,

Have you or your grad student noticed the example got by taking as your
locally presentable category C the category of sets, and as your monad M the
ultrafilter or Stone-Cech monad ß (with the Eilenberg-Moore category of
ß-algebras being the category of compact Hausdorff spaces (and continuous
maps))?

Here, your "objects those X in C such that the unit X -> MX is an isomorphism"
are just the finite sets, and, unless I misunderstand your limits question, I
fear that only finite limits will work as you desire.

Does that help in any way? Cheers, -- Fred 

---

------ Original Message ------
Received: Fri, 10 May 2013 09:23:34 PM EDT
From: Emily Riehl <eriehl< at >math.harvard.edu>
To: categories< at >mta.ca
Subject: categories: on a subcategory of algebras for a monad

example



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on a subcategory of algebras for a monad

Emily Riehl — 2013-05-10T13:05:44

Hi,

I received the following question from a grad student that I was unable to
answer, but maybe you can (shared with permission). The subcategory Comp_M
he introduces below can equally be defined to be the inverter of the
counit of the monadic adjunction. But I don't see how this universal
property helps understand limits in the subcategory. We suspect a left
adjoint to the inclusion is unlikely.

Can you help? Or have you seen something like this before?

Best,
Emily

***
??
Hi folks,
??
I'm interested in closure properties of a particular subcategory of the
category of algebras of a monad. To be more precise, let C be a locally
presentable category and M be a monad on C. The category of algebras Alg_M
has all limits, and they are computed in C. Denote by Comp_M the full
subcategory of Alg_M of "M-complete objects" (does anyone have a better
name?), with objects those X in C such that the unit X -> MX is an
isomorphism, viewed in the natural way as M-algebras (using the inverse MX
-> X).
??
My question: I

(In)accessible comonads and (non)Grothendieck toposes

David Roberts — 2013-05-09T03:07:21

Hi all,

I am just wondering where it was first stated (for both directions) that the category of coalgebras for a comonad on a Grothendieck topos E is again Grothendieck if and only if the underlying endofunctor of E is accessible. 

A modern argument might go as: the topos of coalgebras is Grothendieck if and only if it is locally presentable if and only if the endofunctor is accessible, the original probably just mentioned preservation of filtered colimits.

Many thanks,

David Roberts

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Reminder: CT2013 abstracts

Tom Leinster — 2013-05-08T14:55:07

Dear all,

This is a reminder that if you wish to take advantage of the extended 1
June deadline for submitting abstracts to CT2013, you are requested to
email me **by 10 May** saying that you intend to submit an abstract.
This is to help with planning.

Abstracts received after 10 May will not be accepted unless you have
emailed before then.  I am acknowledging all such emails, so if you have
written to me and not received a reply, there has probably been a
technological problem - in which case, please try again.

Best wishes,
Tom

Samuel Eilenberg Centenary Conference - Second Announcement

Marek Zawadowski — 2013-05-08T09:34:48

-------- SECOND ANNOUNCEMENT-------------------------------------------------

Dear Colleagues,
below is the Second Announcement of the Samuel Eilenberg Centenary Conference
which will be held in Warsaw, July 22-26, 2013. The organizers cordially
invite you to participate in the event commemorating one of the founders of
our field.

-------- SCIENTIFIC PROGRAM--------------------------------------------------

Ten plenary speakers confirmed their attendance and some titles and abstracts
of their lectures are already posted at:

http://eilenberg100.ptm.org.pl/programme

All participants are welcome to propose contributed talks by filling an
appropriate entry in the registration form and uploading an abstract. Note
that the deadline for submissions of titles and abstracts of the contributed
talks is May 31, 2013.

-------- REGISTRATION--------------------------------------------------------

The organizers of the conference cordially invite you to register for the
meeting at:

http://eilenberg100.ptm.org.pl/re

Re: Internal truth objects

Patrik Eklund — 2013-05-08T05:24:43

Dear All,

The question about "logic 'in' category" sounds very "internal" and
indeed toposes (or topoi, whichever you prefer) come to mind. Subobject
classifiers and truth values dominate, and it first looks
very propositional and then quantifiers are rediscovered. So its
rediscovering first-order 'in' some category, where cartesian closedness
as a criteria already "rings a bell".

On the other hand, if we replace 'in' more with 'with' or 'over', logic
with/over categories, work using category theory as an overall
metaalanguage for logic is e.g. seen in Goguen's (and Burstall's etc.)
institutions and Meseguer's entailment systems (general logic). This
approach then creates the category of logics, and morphisms between
logics is interesting.

Concerning types, type constructors are tricky as they are usually left
out of some signature, so type constructors is a "meta business", and
modern type theory looks they way it does because of this. There are e.g.
informal notions like "soft typing", and many many oth

PhD program in Warsaw

Marek Zawadowski — 2013-05-07T21:05:22

Dear Categorists,

Warsaw Center of Mathematics and Computer Science (WCMCS) has opened
registration for PhD programs in mathematics and computer science at the
University of Warsaw and Mathematical Institute of Polish Academy of
Science. A number of PhD scholarships financed by WCMCS will be awarded to
the most promising graduate students. The details of the program are
available at wcmcs.edu.pl/projects. You can apply on-line at
http: //wcmcs.edu.pl/submit-application/admissions-fellowships
The deadline for application is June 7th, 2013.

Best regards,
Marek Zawadowski


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indexed_vs_fibrations

Eduardo J. Dubuc — 2013-05-07T17:26:45


Pare and Scumacher (SLN 661) among other considerations to justify their
choice of indexed categories (= cloven fibrations) over fibrations say:

   "We have tried to make our theory conform as closely as possible to
actual mathematical practice"

Grothendiek (SGA 1, SLN 224, http://arxiv.org/abs/math/0206203) among
other considerations to justify his choice of fibrations over cloven
fibrations (= indexed categories) say:

"Il est d?ailleurs probable que, contrairement a l?usage encore
preponderant maintenant, lie a d?anciennes habitudes de pensee, il
finira par s?averer plus commode dans les problemes universels, de ne
pas mettre l?accent sur une  solution supposee choisie une fois pour
toutes, mais de mettre toutes les solutions sur un pied d?egalite"

"actual mathematical practice" = "l?usage encore preponderant maintenant"

Grothendieck ads  "lie a d'anciennes habitudes de pensee"

Interesting enough, categorical thinking is hard to swallow.

e.d.


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Re: "Terminolgy" re-visited

Toby Bartels — 2013-05-07T16:15:09

Jean B?nabou wrote in part:



By "pullback", I meant what you above call "2-pull-back" or "pseudo pull-back".
Then Z is again (up to isomorphism) 1.


Using zigzags, one would compose zigzags directly and use no pullbacks.


Indeed, so one must also define natural isomorphism of equivalences.
If you have any difficulty, the answer is in Makkai's anafunctor paper:
http://www.math.mcgill.ca/makkai/anafun/


Nothing is hidden in the nLab.
If it changes, click "History" at the bottom of the page.


--Toby


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"Terminolgy" re-visited

Jean Bénabou — 2013-05-07T08:23:34

Dear all,

I cannot type any form of LaTeX, and do not know the "standard" ways to introduce indices,exponentials and so on, using only the typing which is admitted on this list. Thus I shall use "non standard" notations, very simple, which I shall explain precisely.
If A is a category an object a of A can be identified with a functor "name of a" which I denote by "a": 1 --> A .
If  F: A --> C and G: B --> C are functors I denote by  F/G the comma category they define, and by F//G their
  2-pull-back sometimes called their pseudo pull-back.
I shall call "weak equivalence" a functor F: A --> B  full and faithful and essentially surjective (ff-es) and say that A is weakly equivalent (we) to B if there is such an F. This defines  a preorder relation which I denote by 
W(A,B). It is symmetric iff the Axiom of choice (AC) holds.
A strong equivalence between  A and B is a pair of adjoint functors  F: A --> B  and  F': B --> A  such that the adjunction morphisms are isos. I shall say that  A and B are strongly equi