November 2023 - Categories - categories.org.au

PhD opportunities at the University of Birmingham
by Paul Levy 25 Nov '24

25 Nov '24

* Imminent funding deadline (1 December) - please contact us immediately if you are interested. * Dear all, We invite applications for PhD study at the University of Birmingham. We are a group of (mostly) theoretical computer scientists who explore fundamental concepts in computation. Our work includes category theory, computational complexity, programming language semantics, proof theory, type theory, verification and much else besides. See our webpage, with links to individual researchers, here: https://www.birmingham.ac.uk/research/activity/computer-science/theory-of-c… Information about PhD applications may be found here: https://www.birmingham.ac.uk/schools/computer-science/postgraduate-research… If you are considering applying, please contact any of us. We will be very happy to discuss the opportunities available. Best regards, The Birmingham CS theory group, including:- Benedikt Ahrens Rajesh Chitnis Anupam Das Martín Escardó Eric Finster Dan Ghica Mirco Giacobbe Paul Levy Sonia Marin Sean Moss Jakub Opršal Vincent Rahli Uday Reddy Eike Ritter You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

1 1

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/ ]

3 4

YaMCATS 33 announcement
by Nicola Gambino 30 Nov '23

30 Nov '23

*** Yorkshire and Midlands Category Theory Seminar *** Thursday, 25th January 2024 *** University of Leeds The 33rd meeting of the Yorkshire and Midlands Category Theory Seminar (YaMCATS) will be held at the University of Leeds on 25th January 2024. The speakers will be Clark Barwick (University of Edinburgh) Ana Ros Camacho (University of Cardiff) Giacomo Tendas (Masaryk University / University of Manchester) Please check the YaMCATS website https://conferences.leeds.ac.uk/yamcats/ for further information. YaMCATS is a research network involving the Universities of Leeds, Manchester and Sheffield, supported by the London Mathematical Society. With best regards, Nicola Gambino, also on behalf of João Faria Martins (University of Leeds) and Markus Szymik (University of Sheffield) You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

1 0

CiE 2024: Call for papers
by Benno van den Berg 28 Nov '23

28 Nov '23

CiE 2024: CALL FOR PAPERS Computability in Europe 2024 Twenty years of theoretical and practical synergies Amsterdam, The Netherlands July 08-12, 2024 https://events.illc.uva.nl/CiE/CiE2024/ Submission link: https://equinocs.springernature.com/service/CiE2024 IMPORTANT DATES: Deadline for article submission: February 10, 2024 (AOE) Notification of acceptance: April 20, 2024 Final versions due: May 1, 2024 Deadline for informal presentations submission: May 15, 2024 (The notifications of acceptance for informal presentations will be sent a few days after submission) Early registration before: May 20, 2024 Conference: July 08-12, 2024 GENERAL INFORMATION CiE 2024 will be an anniversary event. It is the 20th conference organized by CiE (Computability in Europe), in the same place as the first edition, Amsterdam. CiE is a European association of mathematicians, logicians, computer scientists, philosophers, physicists and others interested in new developments in computability and their underlying significance for the real world. Previous meetings have taken place in Amsterdam (2005), Swansea (2006), Siena (2007), Athens (2008), Heidelberg (2009), Ponta Delgada (2010), Sofia (2011), Cambridge (2012), Milan (2013), Budapest (2014), Bucharest (2015), Paris (2016), Turku (2017), Kiel (2018), Durham (2019), Salerno (2020, virtually), Ghent (2021, virtually), Swansea (2022) and Batumi (2023). TUTORIAL SPEAKERS Matthew Harrison-Trainor (University of Illinois Chicago) Sonja Smets (University of Amsterdam) INVITED SPEAKERS Arnold Beckmann (Swansea University) Rod Downey (Victoria University of Wellington) Elvira Mayordomo (University of Zaragoza) Alexandre Miquel (Universidad de la RepÃºblica) Monika Seisenberger (Swansea University) Mariya Soskova (University of Wisconsinâ€“Madison) SPECIAL SESSIONS There will be 6 special sessions, including: - Computable aspects of symbolic dynamics and tilings (chairs: Benjamin Hellouin and Ilkka Torma) - Algorithmic randomness and Kolmogorov complexity session (chairs: Rupert HÃ¶lzl abd Denis Hirschfeldt) - Bio-inspired Computation (BiC) - History and Philosophy of Computing (HaPoC) Other topics of the special sessions will be announced soon. CONFERENCE TOPICS The CiE conferences serve as an interdisciplinary forum for research in all aspects of computability, foundations of computer science, logic, and theoretical computer science, as well as the interplay of these areas with practical issues in computer science and with other disciplines such as biology, mathematics, philosophy, or physics. PAPER SUBMISSION THE PROGRAM COMMITTEE cordially invites all researchers, European and non-European, to submit their papers in all areas related to the above for presentation at the conference and inclusion in the proceedings of CiE 2024 at https://equinocs.springernature.com/service/CiE2024 CONFERENCE PROCEEDINGS Papers submitted to the conference proceedings should represent original work, not simultaneously submitted to another journal or conference with formal proceedings. The Program Committee will rigorously review and select submitted papers. Accepted papers will be published as a proceedings volume in the Lecture Notes in Computer Science (LNCS) series from Springer-Verlag. Papers to be considered in the conferences proceedings must be submitted in PDF format, using the LNCS style (available at https://www.springer.com/gp/computer-science/lncs/conference-proceedings-gu…) and must have a maximum of 12 pages, including references but excluding a possible appendix in which one can include proofs and other additional material. Papers building bridges between different parts of the research community are particularly welcome. INFORMAL PRESENTATIONS Continuing the tradition of past CiE conferences, we invite researchers to present informal presentations of their recent work. A proposal for an informal presentation must be submitted via e-mail (e.pimentel(a)ucl.ac.uk<mailto:e.pimentel@ucl.ac.uk>), using the LNCS style file (available at https://www.springer.com/gp/computer-science/lncs/conference-proceedings-gu…) and be 1 page long; a brief description of the results suffices and an abstract is not required. Informal presentations will not be published in the LNCS conference proceedings. Results presented as informal presentations at CiE 2024 may appear or may have appeared in other conferences with formal proceedings and/or in journals. PROGRAM COMMITTEE Contributed papers will be selected from submissions received by the PROGRAM COMMITTEE consisting of: Bahareh Afshari (University of Gothenburg) Nathalie Aubrun (CNRS, UniversitÃ© Paris-Saclay) Marie-Pierre BÃ©al (UniversitÃ© Gustave Eiffel) Benno van den Berg (University of Amsterdam) Sebastian Berndt (University of LÃ¼beck) Patricia Bouyer-Decitre (CNRS) Jin-Yi Cai (University of Wisconsin-Madison) Barbara Csima (University of Waterloo) Gianluca Della Vedova (UniversitÃ degli Studi di Milano-Bicocca) Leah Epstein (University of Haifa) Gilda Ferreira (Universidade Aberta) Yannick Foster (INRIA, Nantes) Lorenzo Galeotti (Amsterdam University College) Mathieu Hoyrup (INRIA, LORIA, Nancy) Jarkko Kari (University of Turku) Julia Knight (University of Notre-Dame) Susana Ladra (Universidade de A CoruÃ±a) Timo Lang (Technische UniversitÃ¤t Wien) Karen Lange (Wellesley College) Florin Manea (University of GÃ¶ttingen) Alexander Melnikov (Victoria University of Wellington) Alberto Naibo (UniversitÃ© Paris 1 PanthÃ©on-Sorbonne) Ludovic Patey (CNRS, UniversitÃ© Paris-CitÃ© co-Chair) Elaine Pimentel (University College London co-chair) CristÃ³bal Rojas (Universidad CatÃ³lica) Viola Schiaffonati (Politecnico di Milano) Paul Shafer (University of Leeds) Reed Solomon (University of Connecticut) Andreas Weiermam (Ghent University) WOMEN IN COMPUTABILITY We are very happy to announce that within the framework of the Women in Computability program, we are able to offer some grants for junior women researchers who want to participate in CiE 2024. Applications for this grant should be sent to Lorenzo Galeotti <l.galeotti(a)uva.nl<mailto:l.galeotti@uva.nl>>, before May 15, 2024 and include a short cv (at most 2 pages) and contact information for an academic reference. Preference will be given to junior women researchers who are presenting a paper (including informal presentations) at CiE 2024. HOSTED BY The event will be held in the Amsterdam University College academic building located at Amsterdam Science Park. We are grateful for support from the University of Amsterdam. ORGANIZING COMMITTEE Bahareh Afshari (University of Gothenburg) Luis Aguilar Suarez (Amsterdam University College) Benno van den Berg (University of Amsterdam) Andrea De Domenico (Vrije Universiteit Amsterdam) Tamara Dobler (Vrije Universiteit Amsterdam) Lorenzo Galeotti (Amsterdam University College -- chair) Yurii Khomskii (Amsterdam University College) Mattia Panettiere (Vrije Universiteit Amsterdam) Benjamin Rin (Universiteit Utrecht) You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

1 0

CATNIP meeting 4 Dec 2023 University of Strathclyde
by Paoli, Simona 24 Nov '23

24 Nov '23

Dear Colleagues, the next meeting of the Categories Networking Project (CATNIP) will take place at the University of Strathclyde on 4 December 2023. The invited speakers are: John Baez (University of California Riverside) Rita Fatimah Ahmadi (Imperial College) Neil Ghani (University of Strathclyde) Dan Marsden (University of Nottingham) Details of the programme and the registration form can be found on the CATNIP website https://sites.google.com/view/catniporg/meetings We look forward to seeing you there. Best wishes, The CATNIP organizers Jules Hedges (University of Strathclyde) Chris Heunen (University of Edinburgh) Tom Leinster (University of Edinburgh) Simona Paoli (University of Aberdeen) The University of Aberdeen is a charity registered in Scotland, No SC013683. Tha Oilthigh Obar Dheathain na charthannas clàraichte ann an Alba, Àir. SC013683. You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

1 0

Topology, Representation Theory and Higher Structures
by Paoli, Simona 23 Nov '23

23 Nov '23

Topology, representation theory and higher structures Newton Institute Satellite programme Sabhal Mor Ostaig - Isle of Skye, Scotland This is the first announcement for a 4-week satellite programme of the Newton Institute that will take place in the Gaelic college Sabhal Mor Ostaig on the Isle of Skye. The first two weeks are designed for collaborative research on the themes of the programme, with minimal planned activities. We can host up to 40 participants during these two weeks. Week 3 will be a workshop targeted at younger mathematicians and others who are interested in learning about the themes of the programme. Two-hour introductory talks will be given every morning during this week. Afternoon contributed talks by the participants will be solicited at a later stage. The following mathematicians have agreed to give the introductory talks: Julie Bergner (Homotopy Theory) Bernhard Hanke (Geometry) Markus Linkelmann (Representation Theory) Christoph Schweigert (Quantum Algebra) Karen Vogtman (Geometric Group Theory) Week 4 will be an international conference, with morning plenary talks and contributed afternoon sessions. The following mathematicians will give plenary talks: Tobias Barthel (Homotopy Theory) Diarmuid Crowley (Geometry) Pavel Etingof (Quantum Algebra) Kathryn Hess (Homotopy Theory) Srikanth Iyengar (Quantum Algebra) Dominic Joyce (Geometry) Kathryn Mann (Geometric Group Theory) Julie Plavnik (Representation Theory) Andrew Putman (Geometric Group Theory) Catharina Stroppel (Representation Theory) The registration link ( https://forms.gle/R7ihUWEbK7wGCrcbA) and more information about the programme can be found at https://www.newton.ac.uk/event/trh/ which will be updated regularly. Registration will close on 31st January 2024. Because of space limitations at the venue, we might not be able to accommodate all applicants. We will respond to all applications in early February, after the registration deadline. Childcare for children age 4 and below may be available. Participants who wish to use this service should register as soon as possible and check the relevant box in the registration form. We expect to be able to support all participants in full or in part, with priority given to early career researchers. Free transportation to and from the venue to Glasgow will be arranged once a week with arrivals planned on Sunday and departures on Saturday. We might also be able to provide transport on Saturday - to be confirmed. For any questions, please contact one of the organisers. The organising committee Tara Brendle (Glasgow) tara.brendle(a)glasgow.ac.uk<mailto:tara.brendle@glasgow.ac.uk> Ran Levi (Aberdeen) r.levi(a)abdn.ac.uk<mailto:r.levi@abdn.ac.uk> Ehud Meir (Aberdeen) ehud.meir(a)abdn.ac.uk<mailto:ehud.meir@abdn.ac.uk> Simona Paoli (Aberdeen) simona.paoli(a)abdn.ac.uk<mailto:simona.paoli@abdn.ac.uk> Ana Ros Camacho (Cardiff) roscamachoa(a)cardiff.ac.uk<mailto:roscamachoa@cardiff.ac.uk> Markus Upmeier (Aberdeen) markus.upmeier(a)abdn.ac.uk<mailto:markus.upmeier@abdn.ac.uk> The University of Aberdeen is a charity registered in Scotland, No SC013683. Tha Oilthigh Obar Dheathain na charthannas clàraichte ann an Alba, Àir. SC013683. You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

1 0

HoTT/UF 2024: First Call for Contributions and Participation
by Jonathan Weinberger 23 Nov '23

23 Nov '23

========================================================== 1ST CALL FOR CONTRIBUTIONS AND PARTICIPATION Workshop on Homotopy Type Theory and Univalent Foundations (HoTT/UF 2024, co-located with WG6 meeting of the EuroProofNet COST action) ========================================================== ------------------------------------------------------------------------ Workshop on Homotopy Type Theory and Univalent Foundations April 2 - 3, 2024, Leuven, Belgium https://hott-uf.github.io/2024/ Co-located with the WG6 meeting of the EuroProofNet COST action April 4 - 5, 2024 https://europroofnet.github.io/wg6-leuven/ ------------------------------------------------------------------------ Homotopy Type Theory is a young area of logic, combining ideas from several established fields: the use of dependent type theory as a foundation for mathematics, inspired by ideas and tools from abstract homotopy theory. Univalent Foundations are foundations of mathematics based on the homotopical interpretation of type theory. The goal of this workshop is to bring together researchers interested in all aspects of Homotopy Type Theory/Univalent Foundations: from the study of syntax and semantics of type theory to practical formalization in proof assistants based on univalent type theory. The workshop will be held in person with support for remote participation. We encourage online participation for those who do not wish to or cannot travel. ================ # Submissions * Abstract submission deadline: January 19, 2024 * Author notification: Mid-February 2024 Submissions should consist of a title and a 1-2 pages abstract, in pdf format, via https://easychair.org/conferences/?conf=hottuf2024. Considering the broad background of the expected audience, we encourage authors to include information of pedagogical value in their abstract, such as motivation and context of their work. ================ # Registration Registration is mandatory with a deadline of 8 March 2024 (AoE). Registration information will be provided shortly. ================ # Program committee * Pierre Cagne (Applachian State University) * Evan Cavallo (University of Gothenburg) * Felix Cherubini (Chalmers University of Technology/University of Gothenburg) * Tom de Jong (University of Nottingham) * Eric Finster (University of Birmingham) * Daniel Gratzer (Aarhus University) * Mitchell Riley (NYU Abu Dhabi) * Michael Shulman (University of San Diego) * Kristina Sojakova (INRIA Paris) * Jon Sterling (University of Cambridge) * Andrew Swan (University of Ljubljana) * Jonathan Weinberger (Johns Hopkins University) ================ # Organizers * Evan Cavallo, evan.cavallo(a)gu.se<mailto:evan.cavallo@gu.se> (University of Gothenburg) * Tom de Jong, tom.dejong(a)nottingham.ac.uk<mailto:tom.dejong@nottingham.ac.uk> (University of Nottingham) * Mitchell Riley, mitchell.v.riley(a)nyu.edu<mailto:mitchell.v.riley@nyu.edu> (NYU Abu Dhabi) * Jonathan Weinberger, jweinb20(a)jhu.edu<mailto:jweinb20@jhu.edu> (Johns Hopkins University) You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

1 0

ItaCa Fest, November 23
by Ivan Di Liberti 21 Nov '23

21 Nov '23

Dear all, I am writing to remind you that on November 23rd, we have ItaCa Fest. In line with the new format, we will have 3 talks, listed below. 15:00 - 15:40 M. Volpe, "Traces of dualizable categories and functoriality of the Becker-Gottlieb transfers" 15:40 - 16:20 S. Henry, "Pro-completion of the category of sets and prodiscrete spaces" 16:20 - 17:00 R. Stenzel, "Homotopy-coherent Category Theory à la Benabou” You can find the abstracts here: https://progetto-itaca.github.io/pages/fest23.html#nov23 The link is the usual. https://cs-ox-ac-uk.zoom.us/j/97878376376?pwd=QithMyt5NzdOeE1EWGJRcjBxamxnU… I also take this opportunity to remind everyone that in December there will be the physical ItaCa event, on which you can find more information at this address: https://progetto-itaca.github.io/ItaCa-23/ Best, the ItaCa people. —————————————— Ivan Di Liberti Postdoc Göteborgs universitet https://diliberti.github.io You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

1 0

Postdoc opening in categorical semantics
by Patricia Johann 18 Nov '23

18 Nov '23

Dear Folks, I have an opening for a postdoc, as described in the ad below. In addition to accepting applications, I will be very happy to respond to informal enquiries about any aspect of the position, from technical ones to ones about life in a beautiful "alternative" mountain town in western North Carolina. Best wishes, -patricia -------- Applications are invited for a postdoctoral researcher position in the Computer Science Department at Appalachian State University. The position is part of an NSF-funded project on deep induction rules for advanced data types, specifically GADTs and inductive families. The project aims to build on recent work on GADTs to understand the settings in which they have well-defined initial algebra semantics, to give well-defined such semantics for them in such settings, and then to use these semantics to derive deep induction rules and parametricity properties for them. A key goal is to understand what deep induction rules and parametricity for GADTs look like. Another is to understand what deep induction rules for inductive families look like --- and, in particular, how they differ from deep induction rules for corresponding GADTs. The ideal applicant will have a strong background in functional (ideally dependently-typed) programming, type theory, and category theory. However, more expertise in one area, coupled with a commitment to developing the required competencies, may compensate for less expertise in the others. The successful applicant will also be excited about working on fundamental research questions on the themes of categorical semantics of advanced data types, and deep induction rules and parametricity for them. Interests in applications and/or formalizing computer science theory in, e.g., Agda, are also very welcome. The successful hire will work on the funded project with Prof. Patricia Johann at Appalachian State University, her students, and collaborating researchers. The duration of the position is initially one year, with guaranteed continuation by mutual agreement. (Previous postdocs have continued in their positions an average of about two years.) The position will start at a mutually agreeable date, ideally on or around 1 September 2024. Compensation will be competitive and commensurate with experience. Interested persons should first contact Patricia Johann at johannp(a)appstate.edu, briefly outlining their academic background and research interests, and why they are interested in the position. A complete application will consist of a cover letter and CV, including contact information for three academic references. Complete applications should be made online at https://appstate.peopleadmin.com/postings/43078 Review of applications will begin on 15 January 2024 and will continue until the position is filled. Appalachian State University is an Affirmative Action/Equal Opportunity Employer. The University does not discriminate in access to its educational programs and activities, or with respect to hiring or the terms and conditions of employment, on the basis of race, color, national origin, religion, sex, gender identity and expression, political affiliation, age, disability, veteran status, genetic information or sexual orientation. Individuals with disabilities may request accommodations in the application process by contacting Patricia Johann. Any offer of employment to a successful candidate will be conditioned upon the University's receipt of a satisfactory criminal background report. You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

1 0

The game of the name: Standard constructions, triples, monads, fundamental constructions
by Michael Barr, Prof. 15 Nov '23

15 Nov '23

People seemed to enjoy my history of the founding of TAC, so I thought you might enjoy my sharing of other historical notes. This construction was introduced in Godement's book Théorie des faisceaux in connection with his resolution of sheaves by "faisceaux mous" (soft sheaves) which are an injective class. He called this "la construction standarde". It is not clear whether this was intended to name them or merely describe them. At any rate, around 1960, Benno Eckmann and his students took as a name and called them standard constructions. One of the students, Peter Huber, told me that they were having trouble, in particular cases, verifying the associative law. And then he noticed that in all the cases he knew, the functor T had the form UF, where F --| U. He wondered if every adjoint pair gave rise to a standard construction and proved that it did. Then another student, Heinrich Kleisli, showed that the converse was also true. That gave us the well-known Kleisli construction. In 1963 Samuel Eilenberg and John Moore published a monograph called Foundations of Relative Homological Algebra in which they used this construction as basic. Only they didn't call them standard constructions; they called them triples. I once asked Sammy why and he replied that it didn't seem like an important concept and it didn't seem worth it to spend a lot of time worrying about the name. This is in stark contrast with the time he and Henri Cartan spent thinking about the name for their basic sequences. There is a story, perhaps apocryphal, that their book was in proof stage before they settled on the exact name. So triple was name Jon Beck and I were using in our joint work on homological algebra. Then in 1966 there was a category meeting in Oberwohlfach and there was a lot of discussion of a better name. The next bit of the story comes out of my extremely fallible memory and could well be mistaken. One day at lunch I was sitting next to Anders Koch and he asked what I thought about the name monad. I thought (and still think!) it was a pretty good name and so he proposed it and the assembled crowd agreed and adopted it. I would have too, but Jon rejected it. Why, I asked him. He did not think it a good name and refused to use it. He said there was no point in replacing one bad name by another. Since we were collaborating and since he was even more stubborn than me, that's they way it was. In our papers, Jon insisted on putting functions to the right of their arguments, just like reverse Polish. Then we stopped collaborating and, by 1980, I think I was about ready to start using monad. But then TTT came along and the alliteration was just too good to pass up. Charles Wells agreed on those grounds. And what about fundamental construction? I spent six and a half months at the ETH in Zurich. A few days after I arrived, I got a phone call from Peter Huber, the aforementioned former student of Eckmann's. He had just received from Math Reviews a paper written by Jean-Marie Maranda that used that term for the concept and Huber asked me if there was any way to stop that proliferation of names. As far as I know, that was the only place that term was ever used. Michael You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

15 21