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  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7733">
    <title>Double groupoids and crossed modules</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7733</link>
    <description>&lt;pre&gt;Hi,

In clearing out my office at Bangor University (which for two years or
more I have hardly used) I came across the  first version of my work
with Chris Spencer;   this  was rejected by Saunders for JPAA, after two
negative reports (one described it as "good file drawer stuff",  and the
other remarked that part was known to Verdier and not published. So it
was eventually revised into 2 papers, and published elsewhere, in 1976.
I decided to scan it to have it on my files, and in case anyone else was
interested. It contains some accounts of homotopies and  a Whitehead
theorem, not published elsewhere, except as part of work in the mid
1980s with Philip Higgins. So this is now available,  as they say "as
is", on my preprint page,

http://pages.bangor.ac.uk/~mas010/brownpr.html
&amp;lt;http://pages.bangor.ac.uk/%7Emas010/brownpr.html&amp;gt;

which also has a recent  presentation on John Robinson, sculptor.

Ronnie

&lt;/pre&gt;</description>
    <dc:creator>Ronnie Brown</dc:creator>
    <dc:date>2013-05-24T15:18:08</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7731">
    <title>PhD positions in bialgebraic semantics in Warsaw</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7731</link>
    <description>&lt;pre&gt;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&lt;/pre&gt;</description>
    <dc:creator>Bartek Klin</dc:creator>
    <dc:date>2013-05-22T22:01:25</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7730">
    <title>Post-doctoral Position at the University of Cambridge</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7730</link>
    <description>&lt;pre&gt;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


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

&lt;/pre&gt;</description>
    <dc:creator>Pierre Clairambault</dc:creator>
    <dc:date>2013-05-22T10:45:51</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7729">
    <title>samson&lt; at &gt;60, 28-30 May 2013 Full Program</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7729</link>
    <description>&lt;pre&gt;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 &amp;lt;destiny.chen&amp;lt; at &amp;gt;cs.ox.ac.uk&amp;gt; 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 &amp;amp; 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
&lt;/pre&gt;</description>
    <dc:creator>Bob Coecke</dc:creator>
    <dc:date>2013-05-22T11:18:28</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7728">
    <title>Call for Papers- special issue APAL</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7728</link>
    <description>&lt;pre&gt;

-------------------------------------------------------------------------
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&amp;lt; at &amp;gt;math.unipd.it
-----------------------------&lt;/pre&gt;</description>
    <dc:creator>Maria Emilia Maietti</dc:creator>
    <dc:date>2013-05-18T08:35:18</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7725">
    <title>CT2013 - early bird registration</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7725</link>
    <description>&lt;pre&gt;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)

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

&lt;/pre&gt;</description>
    <dc:creator>Richard Garner</dc:creator>
    <dc:date>2013-05-16T09:46:08</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7723">
    <title>GlynnFest Workshop, May 31st and June 1st, Cambridge University Computer Laboratory</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7723</link>
    <description>&lt;pre&gt;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&lt;/pre&gt;</description>
    <dc:creator>hilde&lt; at &gt;itu.dk</dc:creator>
    <dc:date>2013-05-14T09:27:38</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7721">
    <title>Zig Zags?</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7721</link>
    <description>&lt;pre&gt;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 &lt;/pre&gt;</description>
    <dc:creator>majordomo&lt; at &gt;mlist.mta.ca</dc:creator>
    <dc:date>2013-05-13T12:50:57</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7718">
    <title>on a subcategory of algebras for a monad</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7718</link>
    <description>&lt;pre&gt;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 -&amp;gt; MX is an
isomorphism, viewed in the natural way as M-algebras (using the inverse MX
-&amp;gt; X).
??
My question: I&lt;/pre&gt;</description>
    <dc:creator>Emily Riehl</dc:creator>
    <dc:date>2013-05-10T13:05:44</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7717">
    <title>(In)accessible comonads and (non)Grothendieck toposes</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7717</link>
    <description>&lt;pre&gt;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

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

&lt;/pre&gt;</description>
    <dc:creator>David Roberts</dc:creator>
    <dc:date>2013-05-09T03:07:21</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7716">
    <title>Reminder: CT2013 abstracts</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7716</link>
    <description>&lt;pre&gt;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


&lt;/pre&gt;</description>
    <dc:creator>Tom Leinster</dc:creator>
    <dc:date>2013-05-08T14:55:07</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7715">
    <title>Samuel Eilenberg Centenary Conference - Second Announcement</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7715</link>
    <description>&lt;pre&gt;-------- 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&lt;/pre&gt;</description>
    <dc:creator>Marek Zawadowski</dc:creator>
    <dc:date>2013-05-08T09:34:48</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7713">
    <title>PhD program in Warsaw</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7713</link>
    <description>&lt;pre&gt;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


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

&lt;/pre&gt;</description>
    <dc:creator>Marek Zawadowski</dc:creator>
    <dc:date>2013-05-07T21:05:22</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7709">
    <title>"Terminolgy" re-visited</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7709</link>
    <description>&lt;pre&gt;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 --&amp;gt; A .
If  F: A --&amp;gt; C and G: B --&amp;gt; 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 --&amp;gt; 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 --&amp;gt; B  and  F': B --&amp;gt; A  such that the adjunction morphisms are isos. I shall say that  A and B are strongly equi&lt;/pre&gt;</description>
    <dc:creator>Jean Bénabou</dc:creator>
    <dc:date>2013-05-07T08:23:34</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7704">
    <title>Foundations of Health Information Engineering and Systems (FHIES 2013) - extended submission deadline</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7704</link>
    <description>&lt;pre&gt;THIRD AND FINAL CALL FOR PAPERS

Third International Symposium on
Foundations of Health Information Engineering and Systems
http://www.cs.ox.ac.uk/FHIES2013/

International Institute for Software Technology
United Nations University, Macau
21st-23rd August, 2013


EXECUTIVE SUMMARY - CHANGES SINCE PREVIOUS CALL

Submission deadline extended by two weeks, to May 20th.
Additional category of extended abstracts (max 2 pages) solicited.
Apologies for duplication.


BACKGROUND

ICT plays an increasingly enabling role in addressing the global challenges of healthcare, in both the developed and the developing world. The  use of software in medical devices has caused growing concerns in relation to safety and efficacy. The increasing adoption of health information systems provides great potential benefits but also poses severe risks, both with respect to security and privacy and in regard to patient safety. Hospital and other information systems raise important issues of workflow support and interoperability. Regula&lt;/pre&gt;</description>
    <dc:creator>Jeremy.Gibbons&lt; at &gt;cs.ox.ac.uk</dc:creator>
    <dc:date>2013-05-03T14:55:13</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7703">
    <title>Professorship in Mathematics with focus on Geometry (Stockholm University)</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7703</link>
    <description>&lt;pre&gt;

This position at our department may be of interest to some readers of this list. 
(For instance the geometry research in Sergei Merkulov's group has a quite 
categorical flavour.)

Professor in Mathematics with focus on Geometry

Deadline for application: August 15, 2013.

The Department of Mathematics at Stockholm University with its excellent research record and long lasting traditions has acquired a very special place in Scandinavian mathematics. Professors and lecturers working at the department possess competence in different areas of mathematics ranging from algebra, geometry and analysis to mathematical logic and combinatorics. Geometry with its central role in mathematics has shaped the department’s profile and unites different research groups. We are looking for a mathematician with outstanding research record working in geometry in a broad sense.


http://www.su.se/english/about/vacancies/lecturers-researchers/professor-in-mathematics-with-focus-on-geometry-1.123282

http://eims.ams.org/jobs#/d&lt;/pre&gt;</description>
    <dc:creator>Erik Palmgren</dc:creator>
    <dc:date>2013-05-03T13:36:21</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7702">
    <title>Internal truth objects</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7702</link>
    <description>&lt;pre&gt;Dear categorists,

A standard method for doing logic in category theory is, as far I as
know, by imposing more and more conditions on the subobject posets
Sub(X), which are equivalence classes of monomorphisms with X as the
codomain.

By adding more and more assumptions of this kind one gets more and more
powerful internal logics. The connection between predicates and
functions does not arise in all these stages as long as one does not
request existence of the subobject classifier (therefore almost
certainly turning the whole thing into a topos).

What I am wondering about is whether an alternative approach have ever
been developed, namely by postulating an internal truth-value object
Omega, by introducing predicates as exponentials Omega^X, and so forth.

I would expect, if such an idea have ever been developed it would yield
one of the many ways to provide foundations to the topos theory. The
fact that is not well-known sort of indicates that it is probably not
such a robust idea, in which case I would be &lt;/pre&gt;</description>
    <dc:creator>Sergey Goncharov</dc:creator>
    <dc:date>2013-05-03T15:46:05</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7698">
    <title>LICS 2013 - Call for Participation</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7698</link>
    <description>&lt;pre&gt;***********************************************************************
28th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2013)

June 25-28, 2013
(with pre-conference tutorials on June 24)

New Orleans, USA

Call for Participation
http://lii.rwth-aachen.de/lics/lics13/
***********************************************************************

The twenty-eighth ACM/IEEE Symposium on Logic In Computer Science (LICS 2013)
will be held in New Orleans in colocation with MFPS (Mathematical Foundations
of Programming Semantics) and CSF (IEEE Computer Security Foundations).

* DATES: MFPS (June 23-25), LICS (June 25-28), CSF (June 26-28).

* REGISTRATION is now open for all three conferences.

   Please visit http://lii.rwth-aachen.de/lics/lics13/ and follow the
link to Registration.
   The early registration deadline is May 22, 2013.

* LICS SCHEDULE

   - TUTORIALS
     LICS'13 will kick off with tutorials by Hubert Comon
     and Jan Rutten (with MFPS) on Monday 24 June.

   - TECHNICAL PROGRAMME
  &lt;/pre&gt;</description>
    <dc:creator>Andrzej Murawski</dc:creator>
    <dc:date>2013-05-02T23:25:20</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7696">
    <title>announcement</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7696</link>
    <description>&lt;pre&gt;Dear Colleagues,

I am pleased to inform you that George Janelidze has been just elected
Academician of the Georgian National Academy of Sciences.

With best wishes

Hvedri Inassaridze



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

&lt;/pre&gt;</description>
    <dc:creator>Hvedri Inassaridze</dc:creator>
    <dc:date>2013-05-03T05:22:39</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7689">
    <title>CT2013 abstracts</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7689</link>
    <description>&lt;pre&gt;Dear all,

The original deadline for submitting abstracts to Category Theory 2013
(Macquarie University, Sydney) was 1 May.

This has now been extended to 1 June.  However, if you have not already
submitted an abstract and intend to do so, please email me by 10 May
declaring your intention to submit.

Abstracts themselves should be submitted via the conference website,

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

Best wishes,
Tom Leinster (on behalf of the scientific committee)




&lt;/pre&gt;</description>
    <dc:creator>Tom Leinster</dc:creator>
    <dc:date>2013-05-01T20:29:23</dc:date>
  </item>
  <item rdf:about="http://comments.gmane.org/gmane.science.mathematics.categories/7688">
    <title>Terminology:  Remarks</title>
    <link>http://comments.gmane.org/gmane.science.mathematics.categories/7688</link>
    <description>&lt;pre&gt;Dear all,

Let me first thank the persons who have answered my questions on terminology.
Since the answers were different, it seems that the terminology is not standard and that my questions made sense.

Preliminary remarks. 
By now, everybody understands what kind of categories I was talking about. they are very simple, one might be tempted to say trivial. But in many highly non trivial questions they appear either as "building bricks" of more complex constructions (see e.g. fibrations such that all the fibers are of that kind), or as special cases, unavoidable, of more general situations (e.g. Freyd's notion of "equivalence kernels").
Of course such categories can be "internalized ", say in a topos, (this is much too strong), and it would be nice that the terminology should fit also the internal case, and in particular any reference, explicit or implicit, to AC should be avoided.

1- Discrete versus indiscrete, or coarse, etc. The categories  0 and 1 are both discrete and indiscrete So each name night pose&lt;/pre&gt;</description>
    <dc:creator>Jean Bénabou</dc:creator>
    <dc:date>2013-05-01T05:17:16</dc:date>
  </item>
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