gmane.science.mathematics.categories

MPC2012 Call for Participation

2012-05-23T21:35:01

CALL FOR PARTICIPATION

11th International Conference on Mathematics of Program Construction (MPC  2012)
Madrid, Spain, 25-27 June 2012

http://babel.ls.fi.upm.es/mpc2012

Hotel rooms reserved until:  *** 30th May 2012 ***
Early registration deadline: *** 6th June 2012 ***


BACKGROUND

The biennial MPC conferences aim to promote the development of
mathematical principles and techniques that are demonstrably practical
and effective in the process of constructing computer programs,
broadly interpreted. The 2012 MPC conference will be held in Madrid,
Spain, from 25th to 27th June 2012.


VENUE

The conference will take place in Madrid, the capital of Spain, in the
Sala de Grados of the Facultad de Informática of Universidad
Complutense de Madrid, right in Madrid's Ciudad Universitaria (city
campus), not far from the city centre and other major tourist
attractions. Accommodation has been reserved in a nearby 4-star hotel,
the VP Jardin Metropolitano.


REGISTRATION

Conference registration is now open; see

Re: Bourbaki & category theory

George Janelidze — 2012-05-23T11:36:34

I am ready to take back my criticism and apologize, if the "longer sentence" 
is correct. But is it?

I am certainly not an expert in Bourbaki history, and, as far as I remember, 
they say no word about morphisms in the historical part of "Theory of Sets" 
and give no references on categories. But I think they "always" believed 
that structures determine isomorphisms but not morphisms, and I don't think 
they changed their mind between 1951 and 1957.

When I say "they" I mean "those of them who made main decisions about the 
Bourbaki tractate". Because I hope (!) that not all of them were happy that 
categories are not even defined in the tractate.

In my previous message I wrote "Removing Bourbaki's formalism..." but in 
fact that "formalism" is (not nice but) serious, in the sense that it takes 
us further away from abstract categories.

Anyway, we need to know, if it is still possible, how exactly did Bourbaki 
definition of morphism(s) came up.

George

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

Re: Bourbaki & category theory

Colin McLarty — 2012-05-22T23:06:38

It would not be good -- unless it was part of a longer sentence.

I wrote "Prior to encountering category theory, Bourbaki had a notion
of isomorphism but no general notion of morphism."  The Bourbaki
passage you quote was first published in 1957, at least 6 years after
Bourbaki encountered category theory as shown by the letter from Weil
that i quoted.

best, Colin



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

Re: Derived cotriples

Donovan Van Osdol — 2012-05-22T22:35:25

In my 1969 Ph.D. thesis I showed that, given a "good category for
sheaf theory" and a topological space, the associated sheaf functor
arises as the dual of your construction.  Basically, I needed the
"goodness" hypothesis so that the equalizer itself would construct the
associated sheaf and thus I would not need to iterate your
construction.  The triple used, in this case, was the original
Godement standard construction.  Details can be found in Springer
Lecture Notes in Mathematics, volume 236.

Don


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

Re: Bourbaki & category theory

George Janelidze — 2012-05-22T21:51:28

Dear Colleagues,

I don't think it is good to say that "Bourbaki had a notion of isomorphism 
but no general notion of morphism", even in a brief message!

Bourbaki introduces morphisms in subsection 1 of section 2 of Chapter IV of 
"Theory of Sets". Removing Bourbaki's formalism, the definition can be 
stated as follows:

Let S be a class of mathematical structures of a given type, and let us 
assume for simplicity that these structures have single underlying sets 
(Bourbaki also makes this assumption, also just for simplicity). An element 
of S is therefore a pair (x,s), where x is a set and s a structure on x. By 
a map f : (x,s) --> (y,t) we shall mean an arbitrary map f from x to y. But, 
just as in category theory, a map (x,s) --> (y,t) should "remember" (x,s) 
and (y,t). A class M of such maps is said to be a class of morphisms if it 
satisfies the following conditions:

(i) If f : (x,s) --> (y,t) and g : (y,t) --> (z,u) are in M, then so is gf : 
(x,s) --> (z,u);

(ii) let f : (x,s) --> (y,t) be a ma

Re: Bourbaki & category theory

Ross Street — 2012-05-22T21:45:16


Perhaps relevant (categories vs Bourbaki) is my memory that Sammy Eilenberg 
told me he and Chevalley invented the words injective, surjective and
bijective (as pertaining to functions) while strolling along a beach.

Also I heard Dieudonné admit that Bourbaki would have profited at least from the 
categorical notion of duality. 

==Ross

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

Re: Derived cotriples

Ross Street — 2012-05-22T21:37:44


Brian Day made good use of that construction to revisit the Applegate-Tierney tower.
That might be relevant to Mike Barr too.
See 
Day, Brian. On adjoint-functor factorisation. 
Category Seminar (Proc. Sem., Sydney, 1972/1973), pp. 1--19. 
Lecture Notes in Math., Vol. 420, Springer, Berlin, 1974.

Ross

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

Re: Bourbaki & category theory

Eduardo J. Dubuc — 2012-05-22T17:49:05

The reason why category theory "is what it is" is that

it is the language that allows to define the notion of universal 
property in its right generality.

The notion of universal property first appears in Bourbaki, which 
decided not to use the language of categories to formulate it, on spite 
of the advice of Grothendieck.

e.d


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

Re: Derived cotriples

Eduardo J. Dubuc — 2012-05-22T17:41:08

Hi, the following is related (or the same ?):

In my thesis (SLN 145, page 135) I consider the dual case of
monads=triples in the enriched V-category case.

Considering triple T in A (with the smallness (*) condition of being the
codensity triple determined by a set of objects in A).

I construct a chain of categories

B=A_oo ---> ... ---> A_a ---> .... ---> A_b ---> ... A_1 ---> A_0=A

where A_1 is the category of algebras for the triple T in A

A_(a+1) ---> A_a ,  A_(a+1) is algebras for a triple in A_a

for a limit ordinal a,  A_a is a limit of the preceeding chain of rigth
adjoints.

B is the limit of the large tower over all the ordinals, which is shown
to exists (see (*)).

We have  for all "a"  a rigth adjoint functor  A_a ---> A determining a
triple T_a in A and also a rigth adjoint functor  B ---> A, which is
full and faithful and so the corresponding cotriple in B is the
identity, and the corresponding triple T_oo in A is idempotent. There
are maps of triples:

     T_oo ---> ... ---> T_a ---> ...

Re: Bourbaki & category theory

Colin McLarty — 2012-05-22T17:25:23

Prior to encountering category theory, Bourbaki had a notion of
isomorphism but no general notion of morphism.  See this letter from.
Andre Weil to Claude Chevalley, Oct. 15, 1951:

\begin{quotation} As you know, my honorable colleague Mac~Lane
maintains every notion of structure necessarily brings with it a
notion of homomorphism, which consists of indicating, for each of the
data that make up the structure, which ones behave covariantly and
which contravariantly [\dots] what do you think we can gain from this
kind of consideration? (quoted in Corry  ~\cite[p. 380] Modern Algebra
and the Rise of Mathematical Structures}, Basel: Birkh{\"a}user
1996.\end{quotation}



On Mon, May 21, 2012 at 6:49 PM, Staffan Angere
<Staffan.Angere< at >fil.lu.se> wrote:


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

Re: Derived cotriples

Prof. Peter Johnstone — 2012-05-22T16:34:25

The dual construction was studied by Sabah Fakir in "Monade idempotente
associee a une monade", C.R. Acad. Sci. Paris 270 (1970), A99-101.

Peter Johnstone

On Mon, 21 May 2012, Michael Barr wrote:



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

Bourbaki & category theory

Staffan Angere — 2012-05-21T22:49:24

Dear categorists,

and also, hello everyone, since this is my first post here! I'm wondering about the connection of Bourbaki to category theory. The copy of "Theory of Sets" that I have says it's written in 1970. Yet, Dieudonné famously saiid that the theory of functors subsumed Bourbaki's theory of structures... and, also, Bourbaki's theory of structures is very clearly a theory of a type of concrete categories. On the other hand, I've seen claims that the categorists' use of "morphism" comes from Bourbaki. So who was first? Does anyone here know when Bourbaki's theory of structures was really conceived? I guess this might be self-evident to anyone born during the 1st half of the 20th century, but it has turned out to be really hard to find out for me.

Thanks in advance,
staffan

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

Derived cotriples

Michael Barr — 2012-05-21T21:23:29

Suppose (G,\epsilon,\delta) is a cotriple on a complete category.  Let G^2
===> G ---> G' be a coequalizer.  Then we can find canonical (perhaps
unique) \epsilon':  G' ---> Id and \delta':  G' ---> G'^2 such that
(G',\epsilon',\delta') is a new cotriple on the category and such that G
---> G' is a map of cotriples. It seems reasonable to call this the
derived cotriple.  This process can be repeated, apparently forever, using
colimits at limit ordinals.  If it ever stablizes, the resultant cotriple
will be idempotent and vice versa. Does any know whether this construction
has been studied before?

Michael

Wessex Theory Seminar, Bath, 23rd May

Anupam Das — 2012-05-21T12:09:30

Dear all,

A reminder that the 14th Wessex Theory Seminar will be taking place at
the University of Bath on 23rd May (this Wednesday).

If you plan to attend please reply to this message so I can put you on
the attendance list. As usual there is funding available to reimburse
travel expenses etc.

The preliminary programme is below, and further information can be found
on the website:
https://wiki.bath.ac.uk/display/wessex/14th+Wessex+Theory+Seminar .

The Wessex Theory Seminars are a series of workshops focussed on
theoretical computer science, and in particular mathematical foundations
of programming languages. It is designed to be a joint seminar
of Mathematics and Computer Science departments, and industrial
collaborators. More information about the series can be found on the
website: https://wiki.bath.ac.uk/display/wessex/Wessex+Theory+Seminar .

PRELIMINARY PROGRAMME

10:30 Coffee
11:00 Olle Fredriksson, Birmingham
11:45 Georg Struth, Sheffield
12:30 Lunch
13:45 Alessio Guglielmi, Bath
14:30 James Dave

Re: Hermann Weyl

William Messing — 2012-05-20T16:16:52

Perhaps the closest that Weyl came to discussing things related to
categories and functors is in his marvellous address at the 1954
International Congress of Mathematicians when he spoke on the work of
the Fields Medal winners, Kodaira and Serre.  As cohomology and sheaves
featured prominently in their work, as well of course as spectral
sequences (at least in Serre's work), his writtren text, according to a
footnote more expansive than what he said at the Congress, goes quite
far in "explaining" what de Rham cohomology is, what additional
structures result when the manifold is a complex or Kahler  or Hodge
manifold, how there is a great interplay between the analysis of several
complex variables, linear partial differential equations, algebraic
geometry over the complex numbers, the Hirzebruch Riemann-Roch theorem
(which was actually a conjecture of Serre and was, of course, nd
generalized by Grothendieck to a relative statement valid over any base
field), the Serre duality theorem (discussed by Weyl, only

Hermann Weyl

Colin McLarty — 2012-05-20T14:29:50

Is there any known record of Hermann Weyl ever writing or saying
anything about categories and/or functors?

He certainly heard of the Eilenberg-Steenrod axioms, and a few other
uses.  But did he leave any record?

best, Colin


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

Workshop "Réalisabilité in Chambéry #5"

Pierre Hyvernat — 2012-05-16T12:43:59

Hello...

Since some people on this list might be interested by the following 
workshop, here is an official announcement.
Don't hesitate to register, submit a talk or contact me for details.


Pierre

=====

Greetings to all!

This is the second announcement for the fifth workshop 
"Réalisabilité à Chambéry".

This year's workshop will take place from Tuesday the 5th of June to 
Friday the 8th of June.

The invited speakers are:
     - Martin Hofmann (Munich): "Proof-relevant logical relations",
     - Jonas Frey (Paris): "Basic relational objects as an algebraic 
       framework for realizability"
     - Jean-Louis Krivine (Paris): classical realizability, TBA,
     - Alexandre Miquel (Lyon): realizability model for set theory, TBA.

The program will be made available shortly here:
     http://lama.univ-savoie.fr/~hyvernat/Realisabilite2012/program.php

Note that the meeting will start on Tuesday the 5th, at 2'00 pm.



Partial information is gathered on the web page:
      http://lama.univ-savoie.fr/

Publisher including adware with "free sample" PDFs?

Fred E.J. Linton — 2012-05-11T18:20:19

Sheer coincidence? Or intentionally planned spyware installation?

A few moments ago I accepted the (seemingly kind) offer of
World Scientific / Imperial College Press to download sample
pages of their attractive-sounding new physics publication
"More and Different" by Princeton University Physicist Emeritus 
Philip W. Anderson.

As the PDF for the free sample Chapter 1 was downloading, my
installation of Microsoft Security Essentials popped up with a
warning that some "potentially unwanted adware" had just found 
its way onto my machine, in the form of files 

\DLeasy.net-AVM-ref202085\AVMconverter.exe [->(UPX)] and
\DLeasy.net-AVM-ref202085\AVMconverter-bis.exe [->(UPX)]

that serve to install the Adware:Win32/Hotbar (which, selon

http://www.microsoft.com/security/portal/Threat/Encyclopedia/Entry.aspx?name=Adware%3aWin32%2fHotbar&threatid=6204
,

"installs a browser toolbar that works in Internet Explorer 6, 7, 8 and
Firefox 3.6 and 4.0 ... is a multi-component adware program designed to
monitor user's on

Re: almost bi-monoidal categories

Vaughan Pratt — 2012-05-11T06:38:03

Not that this answers your question, but keep an eye out for the related
forms

X x (A + Y) --> (X x A) + Y
and
(X + A) x Y --> X + (A x Y)

in case you run into either one.  These are half of the weak
distributivity laws for linear logic studied by Cockett and Seely a
decade or so ago.

Although full-blown category theory didn't exist in the 19th century it
did have its posetal fragment, and the above first appears in C.S.
Peirce "Note B: The Logic of Relatives", 1883, see p. 456 of Vol. 4 of
Kloesel's "Writings of C.S. Peirce" where x and + are respectively
relative product (i.e. composition in Rel) and its De Morgan dual (with
respect to Boolean complement) relative sum.

Peirce describes them as "two formulae that are so constantly used that
hardly anything can be done without them."  (They also hold for x,+ as
logical or Boolean conjunction,disjunction whence "hardly anything"
could well extend to brushing one's teeth etc, though only your
subconscious would know that.)

The posetal case of the internal

almost bi-monoidal categories

Ondrej Rypacek — 2012-05-09T23:35:10

Dear category theorists

Could anyone kindly help me with the following:
How much is known about categories with

- two monoidal structures
- and a natural transformation (but not isomorphism)  X x Y -> X + Y

I believe this isn't called a bimonoidal category, as we don't have an
iso above (?)


More generally, how about a tricategory with directed interchange law
(X x Y ) + ( W x Z ) -> (X + W) x (Y + Z) ?

Many thanks,
Ondrej


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

Wessex Theory Seminar, Bath, 23rd May

Anupam Das — 2012-05-10T11:29:19

I am happy to announce that the 14th Wessex Theory Seminar will be
taking place at the University of Bath on Wednesday 23rd May.

The Wessex Theory Seminars are a series of workshops focussed on
theoretical computer science, and in particular mathematical foundations
of programming languages. It is designed to be a joint seminar
of Mathematics and Computer Science departments, and industrial
collaborators. More information can be found on the wiki:
https://wiki.bath.ac.uk/display/wessex/Wessex+Theory+Seminar .

We have already lined up the following speakers:

Alessio Guglielmi, Bath
Jim Laird, Bath
Edmund Robinson, QMUL

There is space for 2-3 more talks, so please contact me if you are
interested. Also let me know if you are planning to attend by replying
to this message.

As usual there is funding available to support attendance at the seminar.

Further details will be announced closer to the time; check the wiki for
the latest information:

https://wiki.bath.ac.uk/display/wessex/14th+Wessex+Theory+Semina