R A G Seely

Translation?

The papers below are in PDF format.
(Some older ones are converted from ps.gz format, and may look "grainy" on-screen, but they should print well.)

Abstracts of (selected) papers are available, linked via the word "abstract".
A more complete list of publications is also on-line.
My reviews for Math Reviews
Google Scholar profile

My Research Papers On-Line

Papers on linear structure

• Differential Categories Revisited (Blute, R.F., Cockett, J.R.B., Lemay, JS.P., Seely, R.A.G.) (Appl. Categor. Struct. 2019) (Abstract) [ArXiv.org] [Local copy]
• Proof theory of the cut rule (Cockett-Seely) [in "Categories for the Working Philosopher" (OUP, ed. Elaine Landry, 2017)]
• Two categorical approaches to differentiation (Slides of talk at CMS meeting, Montreal, Dec 2015)
• Revisiting the term calculus for proof-nets (Slides of talk at FMCS 2014)
• Cartesian differential storage categories (Blute-Cockett-Seely) (TAC 30(2015)18, pp 620-686) (abstract) [ArXiv.org]
  (Slides of talk at FMCS 2012)   (A slightly modified version was presented at FMCS 2013)
• Linear functors and modal logic (Slides of a talk at FMCS 2011)
• The Faà di Bruno Construction (Cockett-Seely) (TAC 25(2011)15, pp.394-425) (abstract)
  [Slides of talks: CMS10, and FMCS10]   [Expanded version for McGill talk]
• Kähler Categories (Blute-Cockett-Porter-Seely) (Cahiers, Volume LII (2011) 253-268) (abstract)
• Cartesian differential categories (Blute-Cockett-Seely) (TAC 22(2009)23, pp.622-672) (abstract)   [ps.gz]
  [Slides for talk at CT07:  [Full size]  [2-up version]]
• Differential Categories (Blute-Cockett-Seely) (MSCS 16(2006) pp 1049-1083) (abstract)
  [Slides of CMS06 talk]   [Slides of CT06 talk]
• Polarized category theory, modules, and game semantics (Cockett-Seely) (TAC 18(2007) pp 4-101)  (abstract)   ["2-up version"]   [Slides of FMCS04 talk]
• Coherence of the Double Involution on *-Autonomous Categories (Cockett-Hasegawa-Seely) (TAC 17(2006) pp 17-29)  (abstract)
• Modules (Cockett-Koslowski-Seely-Wood) (TAC 11(2003)17, pp 375-396.) (abstract)
• Morphisms and modules for poly-bicategories (Cockett-Koslowski-Seely) (TAC 11(2003)2, pp 15-74.) (abstract)   (erratum)   ["2-up version"]
• The logic of linear functors (Blute-Cockett-Seely) (MSCS: 12(2002)4 pp 513-539.) (abstract)
• Finite sum-product logic (Cockett-Seely) (TAC 8(2001)5, pp 63 - 99) (abstract)
• Introduction to linear bicategories (Cockett-Koslowski-Seely) (abstract) ( "Lambekfest" MSCS:10(2000)2 pp 165-203)
• Feedback for linearly distributive categories: traces and fixpoints (Blute-Cockett-Seely) (abstract) ("Bill(Lawvere)Fest", JPAA:154(2000) pp 27-69.)
• Linearly Distributive Functors (Cockett-Seely) (abstract) ("BarrFest" JPAA:143(1999) pp 155-203.)   [Note change in terminology]
• Weakly Distributive Categories (Cockett-Seely) (JPAA 114(1997)2, pp 133-173; Note: This is the "corrected" version.) (abstract)
• Proof Theory for full intuitionistic linear logic, bilinear logic, and MIX categories (Cockett-Seely) (TAC 3(1997)5, pp 85 - 131) (abstract)
• Categories for computation in context and unified logic (Blute-Cockett-Seely) (JPAA 116(1997), pp 49-98) (abstract) (An earlier version is also available (abstract))
• Natural Deduction and Coherence for Weakly Distributive Categories (Blute-Cockett-Seely-Trimble) (JPAA 113(1996)3, pp 229-296) (abstract) [BCST]
• ! and ?: Storage as Tensorial Strength (Blute-Cockett-Seely) (MSCS 6(1996)4, pp 313-351) (abstract)
• Weakly Distributive Categories (Cockett-Seely) (Proceedings of the Durham conference (1991): M.P. Fourman, P.T. Johnstone, A.M. Pitts, eds., Applications of Categories to Computer Science, London Mathematical Society Lecture Note Series 177 (1992) 45 - 65.)  (Corrected version above)
• Polymorphic linear logic and topos models (RAG Seely) (C.R. Math. Rep. Acad. Sci. Canada - Vol. XII, No. 1, February 1990) (abstract)
• Linear logic, *-autonomous categories and cofree coalgebras (RAG Seely) (Contemporary Mathematics, Volume 92, 1989) (abstract)

Papers on Concurrent Constraint Programming

• A Logical View of Concurrent Constraint Programming (Mendler-Panangaden-Scott-Seely) (Nordic J. Computing 2(1995),181-220) (abstract)
• A Hyperdoctrinal View of Concurrent Constraint Programming (Panangaden-Saraswat-Scott-Seely) (Springer LNCS 666)
• A Hyperdoctrinal View of CCP (a slightly expanded version of the above)

Other papers

• Joachim Lambek, FRSC, December 5, 1922 - June 23, 2014 A tribute essay in the Spring 2015 issue of Le Bulletin (21-1), Centre de Recherches Mathématiques (pp 12-13).   [Some photos of Jim]
• A categorical description of the essential structure of differential calculus: a poster for Research Day at John Abbott College, 17 April 2013. (R.A.G. Seely) (Print version)   [The Original A0-size poster]
• Editors' note: bibliometrics and the curators of orthodoxy - Editorial Board of MSCS.  [Full text]
• Models, Logics, and Higher-Dimensional Categories: A Tribute to the Work of Mihàly Makkai. (Bradd Hart, Thomas G. Kucera, Philip J. Scott, Robert A.G. Seely, editors) (CRM Proceedings 53, 2011)
• Language and Grammar: Studies in Mathematical Linguistics and Natural Language. (Claudia Casadio, Philip J. Scott, and Robert A.G. Seely, editors) (CSLI 2005)
  Table of Contents
• The Lambek Program (C. Casadio, P.J. Scott, R.A.G. Seely). (Introduction to the volume above.)
• Fock Space: a Model of Linear Exponential Types (Blute-Panangaden-Seely) (a corrected version of MFPS'93 paper Springer LNCS 802) (abstract)
• A Logical Calculus for Polynomial-time Realizability (Crossley-Mathai-Seely, Methods of Logic in Comp Sci 1 (1994) 279-298) (abstract)
• Category Theory 1991: Proceedings of the 1991 Summer Category Theory Meeting, Montreal, Canada. (R.A.G. Seely, editor, CMS.)
• Graded Multicategories of Polynomial-time Realizers, (R.A.G. Seely, Springer LNCS 389) (abstract)
• Categorical semantics for higher order polymorphic lambda calculus (RAG Seely, JSL 52 (1987) No. 4, 969 - 989   All rights reserved; this reproduction is by special permission for this posting only.)
• Modeling computations: a 2-categorical framework. (RAG Seely, Proc. Symposium on Logic in Computer Science, 1987, Computer Society of the IEEE, 65-71.)
• Locally Cartesian closed categories and type theory. (RAG Seely, Math. Proc. Cambridge Philos. Soc. 95 (1984), no. 1, 33--48.)
• Hyperdoctrines, natural deduction, and the Beck condition. (RAG Seely, Zeitschrift f. math. Logik und Grundlagen d. Math. 29 (1983) 505-542.)
• Weak adjointness in proof theory. (RAG Seely, Proc. Durham Conf. on Applications of Sheaves, SLNM 753 (1979).) ((Most of) the details are in Chapter 1 of my 1977 thesis)

Book Reviews

• Review of Categorical Logic and Type Theory by Bart Jacobs (Review by rags)   PDF version - as published in BSL (BSL 6 (2000) No. 2, 225-229. All rights reserved.)
• Review of Topos Theory by Peter T Johnstone (Review by rags) (JSL 47 (1982) 448 - 450   All rights reserved; this reproduction is by special permission for this posting only.)

Maths and Category Theory Sites

• Some of my coauthors
• Category Theory Research Centre (on WWW.Math.McGill.CA/Triples)
• McGill Mathematics Department
• More Maths links -- Yet More Maths links
• Some Photos from Conferences
• Andrej Bauer's "Photos of Mathematicians" page
• John Abbott College
• Course marks 'n stuff (JAC)

Tools

• Search the web
• Xy-pic (La)TeX diagrams and graphics
  Mike Barr's "front-end" for Xy-pic for categorical diagrams
• TeXCAD (a graphical interface for making diagrams with LaTeX picture mode)
• Lots of (old! LaTeX209) miscellaneous TeX macros and tips
• Sebastian Rahtz's TeX links
• Linear Logic bibliography
• Really Useful Software

Miscellany

• Biometric variability of New Zealand sea lion (Phocarctos hookeri) pups at the Auckland Islands and utility for predicting demographic rates
  (Roberts, J.O.; Cawthorn, M.W.; Childerhouse, S.J.; Clemens-Seely, K. 2021).
• Sediment load and timing of sedimentation affect spore establishment in Macrocystis pyrifera and Undaria pinnatifida
  (Geange, Powell, Clemens-Seely, A. Cárdenas, Marine Biology, 161(7): 1583-1592, July 2014)
• Effects of Temperature on Hatching Time and Hatchling Proportions in a Poecilogonous Population of Haminoea zelandiae
  (Alternate link)  (Clemens-Seely & Phillips, Biol. Bull. 221: 189-196, October 2011).
• Grammy Nominees from McGill, 2016 (Check out Steinberg: Passion Week)
• Info-Cult/Info-Secte (Information about the cult phenomenon - this site has a book (in English and in French, free for download) available on this subject.
• Montreal (tourist info)
• Weather (Canada and elsewhere)
• Parrsboro (Home of the world's highest tides: How High?).
• Ships Company Theatre (Theatre aboard the Kipawo).
• Wild Caraway Restaurant (my favorite restaurant)
• Melbourne
• The "official" Bill Evans homepage
  Two excellent ("former") pages (currently "dormant"!): The Bill Evans Webpages and this (from the waybackmachine) Bill Evans "Time Remembered"
  In the meantime, there's always the Wikipedia page on Evans.
• Basics of the basics of lute continuo (Arto Wikla) (PostScript version typeset by rags)
• Missing page from Koenigsberg MS - TAB source file - Scholarly comments
• J Cohen on "Peirol's Vielle" (PDF from .ps format) - original newsgroup posting
• Yeah³(r.m.b.)
• The Beatles in Canada

The Penrose Quilt

R.A.G. Seely

[]

"In the realm of ideas, of mental objects, those ideas whose properties are reproducible are called mathematical objects, and the study of mental objects with reproducible properties is called mathematics."
- Davis and Hersh (The Mathematical Experience, 1981)

Mathematics is the science which draws necessary conclusions.
- Benjamin Peirce (Linear Associative Algebra, 1870)

The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduced to a Mathematical Reasoning; and when they cannot it's a sign our knowledge of them is very small and confused; and when a Mathematical Reasoning can be had it's as great a folly to make use of any other, as to grope for a thing in the dark, when you have a Candle standing by you.
- John Arbuthnot (Of the Laws of Chance, 1692)

The case for my life, then, or for that of any one else who has been a mathematician in the same sense in which I have been one, is this: that I have added something to knowledge, and helped others to add more; and that these somethings have a value which differs in degree only, and not in kind, from that of the creations of the great mathematicians, or of any other artists, great or small, who have left some kind of memorial behind them.
- G.H. Hardy (A Mathematician's Apology, 1940)

Let no man who is not a Mathematician read the elements of my work.
- Leonardo da Vinci (Notebooks, Introduction)
He who defames the supreme certainty of mathematics feeds on confusion.
- Leonardo da Vinci (Notebooks XIX, 1157)

"What is now proved was once, only imagin'd."
- William Blake (The Marriage of Heaven and Hell, 1790)

A Pale Blue Dot

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