August 2011 - Categories - categories.org.au

Research positions
by Maria Manuel Clementino 26 Feb '14

26 Feb '14

5-YEAR RESEARCH POSITIONS The Centre for Mathematics of the University of Coimbra (CMUC) invites applications for five 5-year research positions in all areas of Mathematics. Applicants should have a PhD in Mathematics and at least three years of post-doctoral experience, with an international-level publication record and demonstrated ability to perform independent research. Preference will be given to candidates working in one of the areas in which the members of CMUC are currently active. A very good command of English is required. The appointments will be made for three years, renewable for two more. Successful applicants are expected to develop research within the areas of interest of CMUC. They should also contribute to graduate studies, supervising students from the Department of Mathematics. The basic salary is equivalent to the index 195 of the Portuguese research career (in the order of 42 500 euros a year), in accordance with the Ciência 2008 guidelines http://alfa.fct.mctes.pt/apoios/contratacaodoutorados/edital2008 Benefits include private health insurance and social security. Applicants should send • cover sheet (available from www.mat.uc.pt/cmuc/coversheet.pdf) including names and contact information of three persons who can provide a letter of recommendation • curriculum vitae (publication list included) • a 5-year research proposal (2 pages max), emphasizing their own research goals as pdf files to cmuc(a)mat.uc.pt. The subject of the e-mail message must include the job reference C2008 FCTUC CMUC v15-v19. The deadline for applications is *September 10, 2008.* ------------------------------ More information can be found at www.mat.uc.pt

1 1

separable locale
by Thomas Streicher 17 May '13

17 May '13

Recently rereading Fourman's "Continuous Truth" I came across the term "separable locale" but could nowhere find an explanation. Does it mean a cHa A for which there exists a countable subset B such that ever a in A is the supremum of those b in B with b leq a. This would be the point free account of "second countable", i.e. having a countable basis. Of course, second countable T_) spaces are separable, i.e. have a countable dense set. Is this reading the "usual" one? Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

5 4

What else do simplicial sets classify?
by Andrej Bauer 05 Oct '11

05 Oct '11

The presheaf category of simplicial sets is the classifying topos for the theory L of a bounded linear order. In general, there could be other theories which are "Morita equivalent" to L in the sense that their classifying toposes are equivalent to simplicial sets. Are any such known, preferably occurring in nature? With kind regards, Andrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

8 7

Octoberfest 2011-Update
by Richard Blute 27 Sep '11

27 Sep '11

UPDATED ANNOUNCEMENT-Octoberfest 2011 The Ocotberfest 2011 website is now up. It can be found at: http://aix1.uottawa.ca/~scpsg/Octoberfest11/Octoberfest11.html * * * The Category Theory "Octoberfest" is an annual workshop, traditionally held in October, bringing together researchers in category theory and its applications. This year's meeting will be hosted in the Department of Mathematics and Statistics at The University of Ottawa, in Ottawa, Ontario. The scientific program starts on October 22, and consists of one and a half days of research talks. Talks: If you wish to give a talk please send a title and abstract to one of the organizers, listed below. Time slots are limited, so please register early if you would like to be considered for a talk. Deadline to send title and abstract is October 1. Accommodations: The website lists a number of hotels and B&Bs. Be sure to book early. Registration If you would like to attend the meeting, please register by emailing one of the organizers. There will be a small on-site registration fee to cover workshop costs. Previous meetings Recent Category Theory Octoberfest meetings were held at Dalhousie (2010), Carnegie Mellon (2009), Concordia (2008), Ottawa (2006 and 2005), McGill (2004). Organizers: Rick Blute: rblute (at) uottawa.ca Pieter Hofstra: phofstra (at) uottawa.ca Phil Scott: phil (at) site.uottawa.ca [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 1

science_publishers
by Eduardo J. Dubuc 06 Sep '11

06 Sep '11

Just thought some in the list may not be aware. Greetings e.d. =============================================================== Von: David Mumford [mailto:dbmumford@gmail.com] Gesendet: Mittwoch, 31. August 2011 18:11 An: Caroline Series; Rob Kirby; Don McClure; Peter J Olver; Martin Groetschel; John Ball; Ingrid Daubechies; Jeremy Mumford; notices(a)math.wustl.edu; vicente.munoz(a)mat.ucm.es; Peter Michor Betreff: Fwd: Elsevier Dear Friends, My son sent me the link below to a very strong and very clear article in the Guardian about the huge fees charged by technical publishers for access to journals. It represents how I have felt for a long time, how the math community among others is being outrageously exploited. I feel it ought to galvanize scientists/mathematicians to react and would like to suggest reprinting it in e.g. the Notices of the AMS, the Newsletter of the EMS, the news email from the IMU, etc. The simple response for mathematicians is to cease submitting any papers to Elsevier or Springer journals. (Excuse me but I am sending this to a somewhat random sample of people that occurred to me and whose email address I had -- eg I don't have an address for Ewing or Friedlander.) yrs faithfully, David http://www.guardian.co.uk/commentisfree/2011/aug/29/academic-publishers-mur… ================================================================= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

10 12

http://www.maths.ed.ac.uk/~aar/giraffe.pdf
by Michael Barr 31 Aug '11

31 Aug '11

I recommend that you go to this site and look at the image. I had photocopied the original New Yorker cartoon and posted it on my bulletin board, giving it the obvious title. Michael -- Any society that would give up a little liberty to gain a little security will deserve neither and lose both. Benjamin Franklin [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

2 1

Grothendieck foundations version 2.0
by Colin McLarty 30 Aug '11

30 Aug '11

Conversations over the summer led to sharp improvements on my February ArXiv article on weak foundations for Grothendieck's number theory. I now formalize the entire Grothendieck tool kit at the strength of finite order arithmetic. In other words at the strength of ETCS (with NNO) or simple type theory with infinity. This includes even the largest scale structures: derived categories for duality, and the 2-category of geometric morphisms between toposes. This does not get as low as n-th order arithmetic for some fixed finite n, but is reasonably weak and yet quite general. This foundation is natural for the Grothendieck toolkit as a whole, while of course no single application uses the whole. Besides that the argument is now simpler, the key advances since my talks in July are: 1) a proof using only bounded separation that every sheaf of modules over any Grothedieck site has an infinite-length injective resolution. Of course the resolution can be 0 from some point on in some cases, but in general it cannot. 2) a conservative extension of Mac~Lane set theory with proper classes and collections of them, modelled on Takeuti's conservative higher order extension of PA. My ArXiv article has been revised. The new version re-titled "A finite order arithmetic foundation for cohomology," is on my web page at http://www.cwru.edu/artsci/phil/Derived_functor.pdf and is on the math arXiv as http://arxiv.org/abs/1102.1773 It is substantially shorter than the February version, while proving a stronger result. I take this as a case where it is easier to prove the right theorem than the wrong one. best, Colin [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0

a coalgebras over fields question.
by Bisson, Terrence P 28 Aug '11

28 Aug '11

Hi, I have heard that naive questions are allowed at the cat list, so here goes: The diagonal map in spaces often gives a co-commutative diagonal map in homology, so I want to understand the special properties of the category of co-commutative coalgebras. It seems to be a "well-known fact" that the category of co-commutative coalgebras over a field is a cartesian closed category, but I can't seem to find much discussion of the internal hom. Can you suggest any reference? Thanks, Terry Bisson [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

6 6

Goursat's lemma
by Michael Barr 27 Aug '11

27 Aug '11

This is something that Lambek used for diagram chasing in his book on Rings and Modules. I have discovered a very simple proof of a slight generalization. The lemma states (as least Jim stated it this way) that if G is a submodule of A x B and C = image of G --> A, C' the image of G --> B, D the kernel of G --> B and D' the kernel of G --> A, then C/D is isomorphic to C'/D'. Forget that G is a subgroup of A x B and just suppose you have two exact sequences 0 --> D' --> G --> C --> 0 and 0 --> D --> G --> C' --> 0, then the composites D --> G --> C and D' --> G --> C' have the same cokernel. The dual claim is that they have the same kernel. But thinking of D and D' are submodules of G, then the kernels are quite obviously D \cap D' and the original conclusion follows by duality. However, the same thing is true for groups (both D and D', being kernels, are normal in G and hence in C, C'). I see no such simple duality argument there. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

2 1

Re: a coalgebra over fields question
by Anders Kock 27 Aug '11

27 Aug '11

Hi, Gavin Wraith lectured in 1976 about an important aspect in this connection. I don't know of any published reference. Namely: The category of commutative algebras is enriched over the cartesian closed category of commutative coalgebras. Does anybody know of a published reference ? (I am in a posoition of a 1981 M.Sc. thesis by Ernst K. Pedersen, giving the details of the constructions involved.) Anders [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

3 2