December 2020 - Categories - categories.org.au

Re: "First" use of 'Category theory' to describe our field
by David Roberts 24 Feb '24

24 Feb '24

Dear Ross, no, that's pretty good! It's mildly surprising that it took ~20 years for the name to 'stick', but maybe less so given that the field grew slowly to start. Thanks, David David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com On Thu, 11 Jul 2019 at 08:21, Ross Street <ross.street(a)mq.edu.au> wrote: > > Dear David > > From memory, the Pure Mathematics Honours (USyd) course that Max Kelly taught in 1965 > was called ``Category Theory''. It concentrated on different kinds of morphisms > and factorizations in a category, and finished with adjoint functors. > Also John Gray's (UIllinois) 1968-69 graduate course had that name. > > From Eilenberg I heard that each person using categories should have their own category of expertise. > I told this to John Gray who said that was fine; the time had come for that category to be Cat. > > I would suggest that the first category theorists to think of themselves as such were Eilenberg's students at Columbia. > However, Mac Lane was definitely a category theorist. > > This is probably not the verifiable stuff you were seeking. > > Ross > > > On 10 Jul 2019, at 10:01 PM, David Roberts <droberts.65537(a)gmail.com> wrote: > > Hi all, > > the (idle) question is: when did the phrase 'category theory' catch on > for the field? Clearly it didn't leap from either of the heads of > Eilenberg or Mac Lane full-grown, since they used the phrase 'General > theory of natural equivalences'. There are the old 'Reports of the > Midwest Category Seminar' lecture notes (the first in 1967), which > hints that 'category theory' wasn't quite the name in use. > > Even more interesting: who was the first "category theorist", by that name? > > Answers referring to verifiable sources would be best. > > Thoughts? > > David > > > > David Roberts > Webpage: https://ncatlab.org/nlab/show/David+Roberts > Blog: https://thehighergeometer.wordpress.com > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Bohemian Logical & Philosophical Café
by Steve Awodey 29 Dec '20

29 Dec '20

CAUTION: The Sender of this email is not from within Dalhousie. Dear Colleagues, I am pleased to announce a new online seminar series: the Bohemian Logical & Philosophical Café. The BLPC is a framework for webinars on current topics in a variety of areas, including theoretical computer science, category theory, mathematical logic, and philosophy. We will start the 26th of January at 16.00 Prague time (GMT+1) with our first speaker: Michael Makkai Notions of identity for and in higher dimensional categories. Further speakers will include: Benno van den Berg, Jouko Väänänen, Jiří Rosický, Jeremy Avigad, André Joyal, and Mike Shulman. Please check our webpage periodically for an updated list of speakers: https://bohemianlpc.github.io With best wishes for the New Year, Steve (for the organizers) [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Categorical Quantum NLP job based at Oxford's new CQC offices.
by Bob Coecke 19 Dec '20

19 Dec '20

CAUTION: The Sender of this email is not from within Dalhousie. Strong Python programming skills, knowledge of NLP and ML are required, and category theory is a major bonus! Here’s the job: https://jobs.eu.lever.co/cambridgequantum/06744371-0e90-4d95-9007-d326504e3… <https://jobs.eu.lever.co/cambridgequantum/06744371-0e90-4d95-9007-d326504e3…> And here is the kind of stuff we do: https://thequantumdaily.com/2020/12/10/meaning-aware-computers-cqc-research… <https://thequantumdaily.com/2020/12/10/meaning-aware-computers-cqc-research…> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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fully funded graduate positions in Math at UWO
by Chris Kapulkin 19 Dec '20

19 Dec '20

CAUTION: The Sender of this email is not from within Dalhousie. Please distribute to undergraduate and master's students and appropriate counsellors and supervisors. Note that we have a large group of faculty, postdocs and graduate students with interests involving homotopy theory, (higher) category theory, and homotopy type theory. Graduate Student Positions Department of Mathematics University of Western Ontario London, Ontario, Canada The Department of Mathematics at the University of Western Ontario solicits applications for its MSc and PhD programs. We have up to 20 fully funded positions available, and applicants from any country are welcome. Our faculty members supervise research in a variety of areas: http://www.math.uwo.ca/graduate/supervisors.html The Department of Mathematics is part of the School of Mathematical Sciences: http://uwo.ca/smss/ More information about our program, including the application procedure, is available at http://www.math.uwo.ca/graduate/ Students normally start in September, in which case applications should be complete (including letters of reference and supplementary material) by February 1. Applications received after this deadline will be reviewed as space permits. Early applications are welcome, and we encourage applicants to apply for external scholarships they are eligible for. Please contact math-grad-program(a)uwo.ca with any questions you may have. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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New journal series: TAC Expositions
by Geoffrey Cruttwell 18 Dec '20

18 Dec '20

CAUTION: The Sender of this email is not from within Dalhousie. The editors of TAC (Theory and Applications of Categories) are pleased to announce a new series of the journal entitled "TAC Expositions". This is a separate series from the standard journal, with a specific focus on expository articles in the theory and applications of categories. The editorial policy of the new series states: "Expositions in Theory and Applications of Categories (`TAC Expositions') is a special series specifically designed for publication of well-written and novel expository articles on topics of current research interest in the theory and/or applications of categories. While a TAC Exposition article need not include new results, it must be novel in either its arrangement or viewpoint, providing a new perspective or context for known results. Authors considering submitting an expository paper are advised to consult an editor on its suitability for TAC Expositions." For more information, see http://www.tac.mta.ca/tac/expositions/index.html. We look forward to receiving your contributions for this new series! All the best, Geoff Cruttwell TAC Managing Editor [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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18th Quantum Physics and Logic (QPL 2021) -- workshop announcement
by QPL 2021 18 Dec '20

18 Dec '20

CAUTION: The Sender of this email is not from within Dalhousie. Dear all, We are delighted to announce the 18th edition of the International Conference on Quantum Physics and Logic (QPL). *QPL 2021* will be hosted by the International Centre for Theory of Quantum Technologies, University of Gdańsk, and take place on *June 7th-11th 2021*, in Gdańsk, Poland. More information may be found at https://qpl2021.eu/ QPL 2021 will feature both an on-site and a virtual component, following the success of the online QPL 2020. Should covid-19 restrictions not allow for the on-site event to happen, QPL 2021 will be hosted entirely in the virtual platform. Important dates to keep in mind: - February 12th: Paper submission deadline, - March 31st: Author notification, - June 7th-11th: The conference. Stay tuned for more information! The list of invited speakers and call for papers will be announced soon. All the best, John Selby and Ana Belen Sainz, on behalf of the Organisers. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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postdoctoral position at ULB
by Joost Vercruysse 16 Dec '20

16 Dec '20

CAUTION: The Sender of this email is not from within Dalhousie. Dear colleagues, Within the framework of the ARC project “From algebra to combinatorics, and back”, financed by the “Fédération Wallonie-Bruxelles" we launch a call for postdoctoral position at the Université Libre de Bruxelles. At least 3 similar calls will be launched over the next 2 years. Profile We look for a strong candidate working in the field of algebra, combinatorics or their interactions. The successful candidate is expected to contribute to the above mentioned research project, under supervision of one or several of the project’s PIs (Michele D’Adderio, Dimitri Leemans, Špela Špenko and Joost Vercruysse). Key-words of the research project are: Non-commutative geometry, noncommutative crepant resolutions, toric varieties, combinatorial representation theory, (partial) representations of groups and Hopf algebras, (partial) actions of groups and Hopf algebras on algebras and abstract polytopes, Tannakian duality, categorification. For more information on the research project, candidates can contact one of the PIs (contact details below). Eligibility PhD: In order to be eligible for this grant, the candidate should have obtained a doctoral degree (PhD or equivalent) strictly before the start of the contract. Mobility constraint: In the last 3 years before the start of the contract, the candidate should not have resided or worked in Belgium for more than 24 months. The contract of the successful candidate can start on any preferred date between March 1, 2021 and June 30, 2021. Our offer The successful candidate will work in the research group “algebra and combinatorics” of the department of Mathematics at the Université Libre de Bruxelles (Brussels, Belgium). There will be a 1-year contract and if both parties are content and the eligibility criteria (see “mobility constraint" above) are still fulfilled, the contract can be renewed for another year. There is a competitive salary (over 2.300 eur Net per month) and the candidate can make use of all facilities of the University. The grant is equipped with a travel grant of 2.500 euro (per year) which the candidate can use to travel and attending conferences or to invite collaborators. Within the research group additional funding is available if there would be more needs. The grant does not come with teaching obligations, although some sporadic (logistic) help for the department (eg. surveillance during exam session) is appreciated. Application procedure To apply for this grant, please send the following data to Joost Vercruysse <jvercruy(a)ulb.ac.be>: . A motivation letter (including a preferred starting date of the contract) . A brief CV, including a publication list and the names and contact details of at least 3 established researchers that can provide a reference letter. Michele D'Adderio <mdadderi(a)ulb.ac.be> Dimitri Leemans <dleemans(a)ulb.ac.be> Špela Špenko <spela.spenko(a)vub.be> Joost Vercruysse <jvercruy(a)ulb.ac.be> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Alternative approach to Stone duality
by tkenney 12 Dec '20

12 Dec '20

Hi. Does anyone know if the following perspective on topology has been studied before (and if so, is there a good reference)? Apologies if I'm missing something very basic here. Let T_0 be the category of T_0 topological spaces and continuous homomorphisms. We have the usual functor (T_0)^op ---> Coframe (this is all 1-dimensional, so you can call it Frame if you prefer) sending a topological space to the coframe of closed sets. This is a faithful fibration. (It can be extended to arbitrary topological spaces, but isn't faithful.) Furthermore, all the non-empty fibres are posets with top elements. These top elements are the sober spaces, and the restriction of the functor to them is full and has an adjoint, which is the usual equivalence between sober spaces and spatial locales. On the other hand, for a large class of coframes (coframes in which every element is a sup of elements which are not _equal_ to the sup of a set of strictly smaller elements), the fibres are complete boolean algebras. Thus the fibres have bottom elements. These are topological spaces where for any point x, x is open in the subspace topology on its closure. Since these spaces are at the bottom of the boolean algebra with sober spaces at the top, they should presumably be called "drunk spaces", though this does lead to there being a large class of spaces which are both sober and drunk. All T_1 spaces are drunk. When restricted to drunk spaces, the functor is not full. However, its image is a subcategory of Coframe (I think the morphisms in the image are complete co-Heyting homomorphisms). When we restrict to this subcategory, we get an equivalence between drunk topological spaces and completely indecomposable-generated coframes with complete co-Heyting algebra homomorphisms. Does anyone know if this duality between "drunk" spaces and indecomposably-generated coframes has been studied? The motivation here is that the fibration extends to a fibration from closure spaces to Inf-lattices, and the usual top element adjoint in this extension is not very interesting, and is on the wrong side for my purposes, but the restricted equivalence above looks like it covers more of the cases of interest. Regards, Toby Kenney [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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The language of diagrams
by Uwe Egbert Wolter 12 Dec '20

12 Dec '20

CAUTION: The Sender of this email is not from within Dalhousie. Dear all, only some weeks ago I became aware of "the language of diagrams" introduced in "Categories, allegories" by Freyd/Scedrov. Two questions: 1. Is this the first place where this language has been described and defined? 2. Has this language been further elaborated and/or applied at other places? Best regards Uwe [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Associate Professorship (~ tenure track faculty) in Programming Languages at Oxford
by Jeremy Gibbons 11 Dec '20

11 Dec '20

CAUTION: The Sender of this email is not from within Dalhousie. The Department of Computer Science at the University of Oxford has an opening for an Associate Professorship and Tutorial Fellowship in Programming Languages. This is the traditional kind of academic position in Oxford, analogous to tenure track in the US. It's at University College, one of the three colleges with claims to be Oxford's oldest, and with one of the colleges with the biggest representation of CS fellows, so you'd be in good company. It includes a significant housing allowance on top of the usual salary. Application deadline is 15th February 2021; interviews are expected to be on 29th March, are likely to be online. I am happy to answer any questions; please do pass on to anyone who might be interested. http://www.cs.ox.ac.uk/news/1870-full.html <http://www.cs.ox.ac.uk/news/1870-full.html> https://my.corehr.com/pls/uoxrecruit/erq_jobspec_details_form.jobspec?p_id=… <https://my.corehr.com/pls/uoxrecruit/erq_jobspec_details_form.jobspec?p_id=…> Jeremy Jeremy.Gibbons(a)cs.ox.ac.uk Oxford University Department of Computer Science, Wolfson Building, Parks Road, Oxford OX1 3QD, UK. +44 1865 283521 http://www.cs.ox.ac.uk/people/jeremy.gibbons/ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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