January 2012 - Categories - categories.org.au

Partial functor
by David Leduc 17 Mar '15

17 Mar '15

Hi, A partial functor from C to D is given by a subcategory S of C and a functor from S to D. What is the appropriate notion of natural transformation between partial functors that would allow to turn small categories, partial functors and those "natural transformations" into a bicategory? The difficulty is that two partial functors from C to D might not have the same definition domain. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

7 6

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

Gowers petition against Elsevier
by Paul Taylor 09 Feb '12

09 Feb '12

http://thecostofknowledge.com/ So far includes Andre Joyal, Jamie Vicary and me from category theory. Others may like to join too. Paul [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

8 8

Re: the cost of knowledge
by Eduardo J. Dubuc 31 Jan '12

31 Jan '12

Registration for library.nu is no longer possible. See: https://www.facebook.com/pages/librarynu/115557691886871 e.d. Library.nu is closed on registration. I have no control over this. Main reason is Library.nu ranked 7th in the world for usage of its type. Now they have legal maters to deal with. They are trimming back there usage by closing registration. However this has not only happening to Library.nu. Its happening all over the web. SOPA and collages are trying to shut down free software sites. SOPA never passed, But is being done under stealth. Next few months you will see less and less of the web free. Government of the United States is after file sharing host. Passing DNS blocks on many countries. The ending goal is the end of the internet as we know it. A move to a internet 2 type system ran by governments of the world. Once there is more using internet 2 and all major search providers switch.(Google, Bing, Aol, Yahoo, Facebook and twitter) They will shut down Internet 1. New system will be a cloud based system where the government can track every file on the web. (Bot AI) Before a file goes to your pc. it must pass threw a cloud system. Before a user can connect to the internet, They will have to go threw valid ID checks on the cloud system. This is a move to control media and the world in the end. We will lose the last freedom we have. Political members of our governments don't work for us. They work for a global agenda to control us all. They must play there parts in censoring the web if they want there power and money in return. (Just greed) If Library.nu ever opened back up registration it will be a miracle. Legal maters is the main key why there can be no invites. If you have an account don't over use it else you will be blocked as well. I have no control over accounts. Nor can I add new members to there site. However this is why I made Essentials For Knowledge. A way for us to still be able to share info and get textbooks and e-books on the web. I have spent the last 2 weeks looking for the best websites. also spent over 80+ hours testing them posting them in a table html. Then answering questions. I spent most of the time searching for these sites. There is 1000s of crappy spam sites out there. Some where not even worth calling an e-book site. All sites I found good where ranked 5 stars max. but if the site was based on what the users really wanted it was ranked 6 stars. Sorry all I can not undo what has been done, however I have not been sitting on my hands :) [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0

Re: cost of knowledge
by Eduardo J. Dubuc 31 Jan '12

31 Jan '12

Please Moderator, let this come across. The subject seems to me pertinent to all mathematicians, including category theorists. In private mail I was told there is already a kind of math-megaupload, the following: <http://library.nu/>. The problem is that to get an account on should be invited. e.d. On 28/01/12 19:27, Joyal, André wrote: > Dear Eduardo, > > Supporting the boycott is probably easier for an established > mathematician like myself > than for a young mathematician without a permanent position. > > On the other hand, solving this problem is important for the young > generation, > since it concerns the scientific life of the future. > > I agree that there are other modes of action, > like putting our papers on the arXiv. I am strongly supporting that. > But it does not address the problem of our libraries which are forced to > spend huge sums of money > to buy knowledges produced by universities, not by publishing houses. > > http://www.guardian.co.uk/commentisfree/2011/aug/29/academic-publishers-mur… > > http://www.guardian.co.uk/science/2012/jan/16/academic-publishers-enemies-s… > > Best, > André [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

2 1

the cost of knowledge
by Joyal, André 30 Jan '12

30 Jan '12

Dear category theorists, This is to let you know (in case you are not) that there is presently a campain to boycott Elsevier. http://thecostofknowledge.com/ Best, André [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

3 3

Good identity
by David Leduc 28 Jan '12

28 Jan '12

Hi, Let F, G, and H be composable functors. I can define the canonical natural transformation from (H o G) o F to H o (G o F) without relying on the evil fact that (H o G) o F = H o (G o F). I just define it componentwisely: for each X, I take id_(H(G(F(X)))). This works in the bicategory of small categories. But now if F, G and H are 1-cells in any bicategory, how can I define the canonical 2-cell from (H o G) o F to H o (G o F) without relying on the evil fact that (H o G) o F = H o (G o F). Thanks! [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 1

product functor, abstractly
by David Leduc 28 Jan '12

28 Jan '12

Hi, In any category with products, one can define the diagonal morphism (from an object X to the object X*X). In the special case of the category of small categories, the above definition gives rise to the diagonal functor (from a category C to the category C*C). How can I in a similar manner define the product functor (from the category C*C to the category C)? I.e. in any category with products, is there a morphism from X*X to X that would give rise to the product functor in the special case of the category of small categories? I guess that I need to assume something on X, but I cannot find the right assumption. Thanks for any help! [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

4 4

An introduction to forms
by Charles Wells 27 Jan '12

27 Jan '12

I have posted here: http://www.abstractmath.org/Word%20Press/?p=3739 an explanation of forms, which I first described in 1990. It contains references to most other papers on the subject. Forms are a generalization of sketches. Charles Wells -- professional website: http://www.cwru.edu/artsci/math/wells/home.html gyre&gimble (math blog): http://www.abstractmath.org/Word%20Press/ abstract math website: http://www.abstractmath.org/MM//MMIntro.htm astounding math stories: http://www.abstractmath.org/MM//MMAstoundingMath.htm personal website: http://www.abstractmath.org/Personal/index.html sixwingedseraph.facebook.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0