January 2023 - 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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Bill Lawvere
by Alberto Peruzzi 20 Feb '23

20 Feb '23

Dear all, a very sad news: Lawvere’s family asked me to provide you with the message below. Alberto Peruzzi Francis William Lawvere (known to most as Bill) died peacefully yesterday (January 23, 2023) at sunrise, surrounded by family at his home in Chapel Hill, North Carolina after a long period of illness. He was born in Muncie, Indiana on Feb. 9, 1937 and has family, friends and colleagues around the world. No services will be held at this time, however several memorial celebrations of life and scientific work are anticipated. Correspondence with family can be sent to his wife Fatima at fatimaylawvere(a)gmail.com <mailto:fatimaylawvere@gmail.com> or to 111 East Winmore Ave., Chapel Hill, NC 27516 USA. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Terminology for point-free topology?
by Steven Vickers 01 Feb '23

01 Feb '23

Dear David, Yes, and it's an excellent paper with a witty title for which only "pointless" would do. I particularly like what Peter said when explaining the significant difference in the absence of choice (such as in toposes of sheaves), and that "usually it is locales, not spaces, which provide the right context in which to do topology". He went on to say, "This is the point which ... Andre Joyal began to hammer home in the early 1970s; I can well remember how, at the time, his insistence that locales were the real stuff of topology, and spaces were merely figments of the classical mathematician's imagination, seemed (to me, and I suspect to others) like unmotivated fanaticism. I have learned better since then." This is all part of the argument for using a reformed topology, but there is nothing particular there about the pointwise style of reasoning for it. Hence we are still left with the question of how to reference the two concepts, the reformed topology and the reasoning without points. Would you call Ng's paper with me pointless? Points are everywhere in it. (Of course, there's the separate issue of whether it was pointless in the sense of not worth the trouble. But an important feature of the style is that it forces you to be careful to distinguish between Dedekind reals and 1-sided (lower or upper) reals, and in Ng's thesis this uncovered unexpected roles of 1-sided reals in the account of Ostrowski's Theorem and the Berkovich spectrum. So there is a bit of payoff.) Best wishes, Steve. ________________________________ From: David Yetter <dyetter(a)ksu.edu> Sent: Friday, January 20, 2023 3:06 AM To: I.Moerdijk(a)uu.nl <I.Moerdijk(a)uu.nl>; Steven Vickers (Computer Science) <s.j.vickers.1(a)bham.ac.uk> Cc: categories list <categories(a)mta.ca> Subject: Re: categories: Re: Terminology for point-free topology? I seem to recall from back in my days as a grad student or new PhD that Peter Johnstone wrote a paper entitled "The Point of Pointless Topology". Just in honor of that I've always favored "pointless topology" as the term for the theory of locales and sheaves on locales. Best Thoughts, David Y. ________________________________ From: Steven Vickers <s.j.vickers.1(a)bham.ac.uk> Sent: Wednesday, January 18, 2023 6:12 AM To: I.Moerdijk(a)uu.nl <I.Moerdijk(a)uu.nl> Cc: categories list <categories(a)mta.ca> Subject: categories: Re: Terminology for point-free topology? This email originated from outside of K-State. Dear Ieke, Thanks for mentioning that. It's a beautiful paper, both in its results and in its presentation, and one I still return to. Another place where I think you were even more explicit was in "The classifying topos of a continuous groupoid I" (1988), where you said - "... in presenting many arguments concerning generalized, "pointless" spaces, I have tried to convey the idea that by using change-of-base-techniques and exploiting the internal logic of a Grothendieck topos, point-set arguments are perfectly suitable for dealing with pointless spaces (at least as long as one stays within the 'stable' part of the theory)." (Would you still say that "pointless" and "point-set" are the right phrases there? I'm proposing "point-free" and "pointwise".) On the other hand, in your book with Mac Lane, those ideas seemed to go into hiding. In fact I explicitly wrote "Locales and toposes as spaces" as a guide to reading the points back into the book. My first understanding of these pointwise techniques came in the 1990's, as I developed the exposition of "Topical categories of domains". That was before I knew those papers of yours, but I felt right from the start that I was merely unveiling techniques already known to the experts - though I hope you'll agree I've been more explicit about them and particularly the nature and role of geometricity. I still don't know as much as I would like about the origin and history of those techniques. It would certainly improve my arXiv notes if I could say more. Might they even have roots in Grothendieck? I once saw a comment by Colin McLarty to the effect that (modulo misrepresentation by me) Grothendieck was aware of two different lines of reasoning with toposes: by manipulating sites concretely, or by using colimits and finite limits under the rules corresponding to Giraud's theorem. I imagine that as being something like the distinction between pointless and pointwise. Best wishes, Steve. ________________________________ Hi Steve, A very early illustration of the strategy of using points in pointless topology is in my paper with Wraith (published 1986). I just looked at it again, and the strategy is explicitly stated in the introduction : "the strategy is to use adequate extensions of the base topos available from general topos theory, which enable one to follow classical arguments about points of separable metric spaces rather closely. Although both approaches are equivalent, we will follow the second one, because it shows more clearly the interplay between general topos theory and arguments (somewhat similar to those) from topology" We used it to prove an actual theorem. Of course I used this strategy much more often, e.g. in my two 1990 papers with Joyal. Ieke [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Sheaves as a localisation of separated presheaves
by Richard Garner 01 Feb '23

01 Feb '23

Hi all, > If (C,J) is a site, then the category Sh(C) can be presented as a > category of fractions Psh(C)[D^-1] where D is the class of J-dense > monomorphisms. Morphisms in here are equivalence classes of partial maps > X --> Y whose domain is dense in X, and where the equivalence relation > is generated by the 2-cells of spans. > > This is all well known. I am wondering if there is a reference for the > following fact: if one restricts to separated presheaves, then every > equivalence class of morphisms has a maximal representative, given by > the dense partial maps X <--< X' ---> Y whose graph X' >---> X*Y is a > J-closed monomorphism. So between separated presheaves, no quotienting > is necessary---beyond that inherent in the notion of subobject---though > now composition is no longer span composition on equivalence classes, > but rather span composition followed by J-closure. Looking more carefully, the proof of this seems to work fine if only Y is separated. So another way of saying the above is that the plus-construction on separated presheaves can be described without taking a quotient. However, thinking about this a bit more I should also fess up that my original statement is in error. Psh(C)[D^-1] is NOT the category of sheaves. It is the result of universally inverting the dense monos, but the category so obtained is not cocomplete. To get a cocomplete category, we need to invert the class of all bidense morphisms. How do we know Psh(C)[D^-1] isn't cocomplete? Well, if it were, then the localisation functor Psh(C) --> Psh(C)[D^-1], which obviously preserves colimits, would necessarily be sheafification Psh(C) --> Sh(C) (by the universal property of the latter), with as right adjoint the singular functor of C --> Psh(C) --> Psh(C)[D^-1]. But the monad induced by this adjunction on Psh(C) would then be the single plus construction, which is well-known not to be the reflector into the category of sheaves. (This had me worried for a while, as it seemed I had come up with an interesting proof of _|_.) On the other hand, it seems to be totally fine to describe Sh(C) as SepPsh(C)[D^-1], because the latter is the Kleisli category for the single-plus construction on SepPsh(C); and then the above quotient-free description does pertain. I realise I am basically talking to myself at this point but figure I should try to set the record straight! Richard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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FSCD 2023: Extended deadline (Abstract: February 4/ Submission: February 9)
by Carsten Fuhs 01 Feb '23

01 Feb '23

============================================================================== Updated information on: EXTENDED DEADLINE for submission ============================================================================== LAST CALL FOR PAPERS Eighth International Conference on Formal Structures for Computation and Deduction (FSCD 2023) July 3-6, 2023, Rome, Italy https://easyconferences.eu/fscd2023/ In-cooperation with ACM SIGLOG and SIGPLAN IMPORTANT DATES --------------- All deadlines are midnight anywhere-on-earth (AoE); late submissions will not be considered. Abstract: EXTENDED to February 4, 2023 Submission: EXTENDED to February 9, 2023 Rebuttal: March 24-28, 2023 (not changed) Notification: April 13, 2023 (not changed) Final version: April 27, 2023 (not changed) CO-LOCATION AND AFFILIATED WORKSHOPS ------------------------------------ FSCD 2023 will be co-located with CADE-29. The following workshops are affiliated with FSCD and CADE in 2023: - WIL: 7th Workshop Women in Logic (July 1, 2023) - WPTE: 10th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (July 1, 2023) - TLLA: 7th International Workshop on Trends in Linear Logic and Applications (July 1-2, 2023) - LSFA: 8th Logical and Semantic Frameworks with Applications (July 1-2, 2023) - DCM: 13th International Workshop on Developments in Computational Models (July 2, 2023) - LFMTP: International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (July 2, 2023) - UNIF: 37th International Workshop on Unification (July 2, 2023) - CASC: The CADE ATP System Competition (July 3, 2023) - HOR: 11th International Workshop on Higher-Order Rewriting (July 4, 2023) - SMT: 21st International Workshop on Satisfiability Modulo Theories (July 4-6, 2023) - ADeMaL: Automated Deduction for Machine Learning (July 5, 2023) - ThEdu: Theorem proving components for Educational software (July 5, 2023) - Vampire: 7th Vampire Workshop (July 5, 2023) - IFIP WG 1.6: Annual Meeting of IFIP Working Group 1.6 on Rewriting (July 5, 2023) OVERVIEW -------- FSCD (https://fscd-conference.org/) covers all aspects of formal structures for computation and deduction from theoretical foundations to applications. Building on two communities, RTA (Rewriting Techniques and Applications) and TLCA (Typed Lambda Calculi and Applications), FSCD embraces their core topics and broadens their scope to closely related areas in logic, models of computation, semantics and verification in new challenging areas. The suggested, but not exclusive, list of topics for submission is: 1. Calculi: - Rewriting systems (string, term, higher-order, graph, conditional, modulo, infinitary, etc.); - Lambda calculus; - Logics (first-order, higher-order, equational, modal, linear, classical, constructive, etc.); - Proof theory (natural deduction, sequent calculus, proof nets, etc.); - Type theory and logical frameworks; - Homotopy type theory; - Quantum calculi. 2. Methods in Computation and Deduction: - Type systems (polymorphism, dependent, recursive, intersection, session, etc.); - Induction, coinduction; - Matching, unification, completion, orderings; - Strategies (normalization, completeness, etc.); - Tree automata; - Model building and model checking; - Proof search and theorem proving; - Constraint solving and decision procedures. 3. Semantics: - Operational semantics and abstract machines; - Game Semantics and applications; - Domain theory and categorical models; - Quantitative models (timing, probabilities, etc.); - Quantum computation and emerging models in computation. 4. Algorithmic Analysis and Transformations of Formal Systems: - Type inference and type checking; - Abstract Interpretation; - Complexity analysis and implicit computational complexity; - Checking termination, confluence, derivational complexity and related properties; - Symbolic computation. 5. Tools and Applications: - Programming and proof environments; - Verification tools; - Proof assistants and interactive theorem provers; - Applications in industry; - Applications of formal systems in other sciences; - Applications of formal systems in education. 6. Formal Systems for Semantics and Verification in new challenging areas: - Certification; - Security; - Blockchain protocols; - Data bases; - Deep learning and machine learning algorithms; - Planning. PUBLICATION ----------- The proceedings will be published as an electronic volume in the Leibniz International Proceedings in Informatics (LIPIcs) of Schloss Dagstuhl. All LIPIcs proceedings are open access. SPECIAL ISSUE ------------- Authors of selected papers will be invited to submit an extended version to a special issue of Logical Methods in Computer Science, or to TheoretiCS. SUBMISSION GUIDELINES --------------------- The submission site is: https://easychair.org/conferences/?conf=fscd2023 Submissions must be formatted using the LIPIcs style files (https://submission.dagstuhl.de/series/details/5#author) and submitted via EasyChair. Submissions can be made in two categories. Regular research papers are limited to 15 pages, excluding references and appendices. They must present original research which is unpublished and not submitted elsewhere. System descriptions are limited to 15 pages, excluding references. Shorter papers are welcome and will be given equal consideration. A system description must present new software tools, or significantly new versions of such tools, in which FSCD topics play an important role. An archive of the code with instructions on how to install and run the tool must be submitted. In addition, a webpage where the system can be experimented with should be provided. One author of each accepted paper is expected to register and present the work in person at the conference. Alternatively to in-person presentation, also online presentation is possible, but in-person registration by at least one author will still be required. BEST PAPER AWARD BY JUNIOR RESEARCHERS -------------------------------------- The program committee will select a paper in which at least one author is a junior researcher, i.e. either a student or whose PhD award date is less than three years from the first day of the meeting. When submitting the paper, other authors should declare to the PC Chairs that at least 50% of contribution is made by the junior researcher(s). PROGRAM COMMITTEE CHAIRS ------------------------ Marco Gaboardi, Boston University Femke van Raamsdonk, Vrije Universiteit Amsterdam Email: fscd2023 at easychair.org PROGRAM COMMITTEE ----------------- Martin Avanzini, INRIA Patrick Bahr, ITU Copenhagen Pablo Barenbaum, University of Quilmes (CONICET) & ICC Filippo Bonchi, University of Pisa Sabine Broda, University of Porto Valeria De Paiva, Topos Institute Andrej Dudenhefner, TU Dortmund Santiago Escobar, Universitat Polit??cnica de Val??ncia Claudia Faggian, University of Paris (IRIF) Frank (Peng) Fu, Dalhousie University Silvio Ghilardi, University of Milano Clemens Grabmayer, GSSI or Gran Sasso Science Institute Nao Hirokawa, JAIST Mirai Ikebuchi, National Institute of Informatics Ambrus Kaposi, Eotvos Lorand University Ian Mackie, University of Sussex Radu Mardare, University of Strathclyde Aart Middeldorp, University of Innsbruck Anders Mortberg, University of Stockholm Daniele Nantes-Sobrinho, Imperial College London / University of Bras??lia Vincent van Oostrom, Independent researcher Grigore Rosu, University of Illinois Urbana-Champaign Luca Roversi, University of Torino Aleksy Schubert, University of Warsaw Jakob G. Simonsen, University of Copenhagen Alwen Tiu, Australian National University Valeria Vignudelli, CNRS/ENS Lyon Johannes Waldmann, HTWK Leipzig Sarah Winkler, University of Bolzano CONFERENCE CHAIR ---------------- Daniele Gorla, University of Rome - Sapienza WORKSHOP CHAIR -------------- Ivano Salvo, University of Rome - Sapienza STEERING COMMITTEE WORKSHOP CHAIR -------------------------------- Cynthia Kop, Radboud University Nijmegen PUBLICITY CHAIR --------------- Carsten Fuhs, Birkbeck, University of London FSCD STEERING COMMITTEE ----------------------- Zena Ariola, University of Oregon Alejandro D??az-Caro, Quilmes University & ICC/CONICET Amy Felty, University of Ottawa Carsten Fuhs, Birkbeck, University of London Herman Geuvers (Chair), Radboud University Nijmegen Silvia Ghilezan, University of Novi Sad J??rgen Giesl, RWTH Aachen University Stefano Guerrini, Universit?? de Paris 13 Delia Kesner, Universit?? de Paris Diderot Naoki Kobayashi, University of Tokyo Cynthia Kop, Radboud University Nijmegen Luigi Liquori, Inria Daniele Nantes, Imperial College London / University of Bras??lia [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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CT Advisory Committee: new Chair
by ptj＠maths.cam.ac.uk 01 Feb '23

01 Feb '23

Having chaired the CT Advisory Committee for 12 years (since the late Bill Lawvere stepped down at the end of 2010), Peter Johnstone has decided that the time has come for him in turn to step down from this role. The other members of the Committee are pleased to announce that Maria Manuel Clementino has agreed to take over; so notice is hereby given that any enquiries or proposals concerning future CT meetings should be addressed to her at mmc(a)mat.uc.pt. The Advisory Committee, which was set up in 2004, exists to offer help and advice to potential organizers of international Category Theory conferences, and to try to ensure that such conferences are held at regular intervals. Peter Johnstone Maria Manuel Clementino [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Terminology for point-free topology?
by Robert Pare 31 Jan '23

31 Jan '23

Dear Steve, I've been following this thread with interest, though I've never worked on the subject. In trying to understand what it's actually all about, I've come to the conclusion that it's "copoint topology". Is that Crazy? Cheers, Bob ________________________________ From: Steven Vickers <s.j.vickers.1(a)bham.ac.uk> Sent: January 23, 2023 9:47 AM To: categories list <categories(a)mta.ca> Subject: categories: Re: Terminology for point-free topology? Dear Pedro, Of course, that's the very reason why I wanted to transfer it to the style of working without points. That's slightly unfair, in that in many cases of reasoning algebraically, without points, it's not at all clear how to do it pointwise. You and I have certainly experienced that in our work on quantales, which are much more purely algebraic gadgets. Our approach via localic suplattices (algebras for the lower hyperspace monad) gives a more point-free approach to the subject, but it takes effort - I think you'll agree - to work with the hyperspaces in a pointwise manner. Do you think there's a less derogatory term for the style of reasoning without points? All the best, Steve. ________________________________ From: pedro.m.a.resende(a)tecnico.ulisboa.pt <pedro.m.a.resende(a)tecnico.ulisboa.pt> Sent: Monday, January 23, 2023 11:44 AM To: ptj(a)maths.cam.ac.uk <ptj(a)maths.cam.ac.uk> Cc: Steven Vickers (Computer Science) <s.j.vickers.1(a)bham.ac.uk>; categories list <categories(a)mta.ca> Subject: Re: categories: Re: Terminology for point-free topology? In addition to all the deeper reasons, `pointless’ can be taken to be derogatory, so preferably it should be used only when in tongue-in-cheek mode. At least that’s what I tell my students — just as I ask them not to say `abstract nonsense’ too enthusiastically… :) Pedro [For admin and other information see: http://www.mta.ca/~cat-dist/ ] --_000_YQXPR01MB2646265C1D8882E80428F9F5E5C99YQXPR01MB2646CANP_ Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=Windows-1252"> <style type="text/css" style="display:none;"> P {margin-top:0;margin-bottom:0;} </style> </head> <body dir="ltr"> <div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof"> <br> </div> <div id="appendonsend"></div> <hr style="display:inline-block;width:98%" tabindex="-1"> <div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Robert Pare <R.Pare(a)Dal.Ca><br> <b>Sent:</b> January 24, 2023 8:19 AM<br> <b>To:</b> Steven Vickers <s.j.vickers.1(a)bham.ac.uk><br> <b>Cc:</b> categories@mta <categories@mta><br> <b>Subject:</b> Re: categories: Re: Terminology for point-free topology?</font> <div> </div> </div> <style type="text/css" style="display:none">  </style> <div dir="ltr"> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> Dear Steve,</div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> <br> </div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> I've been following this thread with interest, though I've never worked</div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> on the subject. In trying to understand what it's actually all about, I've</div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> come to the conclusion that it's "copoint topology". Is that Crazy?</div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> <br> </div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> Cheers,</div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> <br> </div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> Bob<br> </div> <div id="x_appendonsend"></div> <hr tabindex="-1" style="display:inline-block; width:98%"> <div id="x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Steven Vickers <s.j.vickers.1(a)bham.ac.uk><br> <b>Sent:</b> January 23, 2023 9:47 AM<br> <b>To:</b> categories list <categories(a)mta.ca><br> <b>Subject:</b> categories: Re: Terminology for point-free topology?</font> <div> </div> </div> <div class="x_BodyFragment"><font size="2"><span style="font-size:11pt"> <div class="x_PlainText">CAUTION: The Sender of this email is not from within Dalhousie.<br> <br> Dear Pedro,<br> <br> Of course, that's the very reason why I wanted to transfer it to the style of working without points.<br> <br> That's slightly unfair, in that in many cases of reasoning algebraically, without points, it's not at all clear how to do it pointwise.<br> <br> You and I have certainly experienced that in our work on quantales, which are much more purely algebraic gadgets. Our approach via localic suplattices  (algebras for the lower hyperspace monad) gives a more point-free approach  to the subject, but it takes effort - I think you'll agree - to work with the hyperspaces in a pointwise manner.<br> <br> Do you think there's a less derogatory term for the style of reasoning without points?<br> <br> All the best,<br> <br> Steve.<br> <br> ________________________________<br> From: pedro.m.a.resende(a)tecnico.ulisboa.pt <pedro.m.a.resende(a)tecnico.ulisboa.pt><br> Sent: Monday, January 23, 2023 11:44 AM<br> To: ptj(a)maths.cam.ac.uk <ptj(a)maths.cam.ac.uk><br> Cc: Steven Vickers (Computer Science) <s.j.vickers.1(a)bham.ac.uk>; categories list <categories(a)mta.ca><br> Subject: Re: categories: Re: Terminology for point-free topology?<br> <br> In addition to all the deeper reasons, `pointless’ can be taken to be derogatory, so preferably it should be used only when in tongue-in-cheek mode.  At least that’s what I tell my students — just as I ask them not to say `abstract nonsense’ too enthusiastically… :)<br> <br> Pedro<br> <br> <br> [For admin and other information see: <a href="http://www.mta.ca/~cat-dist/">http://www.mta.ca/~cat-dist/</a> ]<br> </div> </span></font></div> </div> </body> </html> --_000_YQXPR01MB2646265C1D8882E80428F9F5E5C99YQXPR01MB2646CANP_-- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Sheaves as a localisation of separated presheaves
by Richard Garner 30 Jan '23

30 Jan '23

Dear all, If (C,J) is a site, then the category Sh(C) can be presented as a category of fractions Psh(C)[D^-1] where D is the class of J-dense monomorphisms. Morphisms in here are equivalence classes of partial maps X --> Y whose domain is dense in X, and where the equivalence relation is generated by the 2-cells of spans. This is all well known. I am wondering if there is a reference for the following fact: if one restricts to separated presheaves, then every equivalence class of morphisms has a maximal representative, given by the dense partial maps X <--< X' ---> Y whose graph X' >---> X*Y is a J-closed monomorphism. So between separated presheaves, no quotienting is necessary---beyond that inherent in the notion of subobject---though now composition is no longer span composition on equivalence classes, but rather span composition followed by J-closure. The proof is rather easy but I am wondering if there is the even easier possibility of citing something. Thanks! Richard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Assistant professor in logic / semantics
by Fokkink, W.J. (WJ) 27 Jan '23

27 Jan '23

The Department of Computer Science at the Vrije Universiteit Amsterdam offers an open position as assistant professor in Theoretical Computer Science, in the area of logic or semantics, broadly construed. https://workingat.vu.nl/ad/assistant-professor-tcs-tenure-track-career-trac… Deadline for application is March 14, 2023. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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lecturer in Computational Linguistics in UCL
by Sadrzadeh, Mehrnoosh 26 Jan '23

26 Jan '23

Dear colleagues, The Linguistics department of University College London (UCL) is recruiting a lecturer (permanent academic post) in Computational Linguistics. For more details of the position, see here: https://www.ucl.ac.uk/work-at-ucl/search-ucl-jobs/details?jobId=3786&jobTit… Best, Mehrnoosh [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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