R A G Seely
Department of Mathematics,
McGill University,
805 Sherbrooke St W,
Montreal, Quebec,
Canada H3A 0B9
My John Abbott
Course Home Page.
Some books to read
My
Principles of Maths and Logic course (for Liberal Arts students)
Chapter 1 of my text for that course
The Liberal Arts at John Abbott
Logic, Category
Theory, and Computation Seminar at McGill
Categorical
and other meetings
Translation?
The papers below are in PDF format.
(Some older ones are converted from ps.gz format, and may look
"grainy" onscreen, but they should print well.)
Abstracts of (selected) papers are available, linked via the word
"abstract".
A more complete list
of publications is also online.
My reviews for Math Reviews
Google
Scholar profile
What is Category
Theory?
My Research Papers OnLine
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 (CockettSeely) [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 proofnets (Slides of talk at FMCS 2014)
 Cartesian
differential storage categories (BluteCockettSeely)
(TAC 30(2015)18, pp 620686)
(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 (CockettSeely) (TAC 25(2011)15, pp.394425)
(abstract)
[Slides of
talks: CMS10, and FMCS10]
[Expanded
version for McGill talk]

Kähler Categories (BluteCockettPorterSeely)
(Cahiers,
Volume LII (2011) 253268)
(abstract)
 Cartesian
differential categories (BluteCockettSeely) (TAC 22(2009)23, pp.622672)
(abstract)
[ps.gz]
[Slides for talk at CT07:
[Full size]
[2up
version]]

Differential Categories (BluteCockettSeely) (MSCS 16(2006) pp 10491083)
(abstract)
[Slides of CMS06 talk]
[Slides of CT06 talk]
 Polarized
category theory, modules, and game semantics (CockettSeely)
(TAC 18(2007) pp 4101)
(abstract)
["2up
version"]
[Slides of FMCS04 talk]
 Coherence
of the Double Involution on *Autonomous Categories
(CockettHasegawaSeely) (TAC 17(2006) pp 1729)
(abstract)
 Modules
(CockettKoslowskiSeelyWood) (TAC 11(2003)17, pp 375396.)
(abstract)

Morphisms and modules for polybicategories
(CockettKoslowskiSeely) (TAC 11(2003)2, pp 1574.)
(abstract)
(erratum)
["2up
version"]

The logic of linear functors (BluteCockettSeely) (MSCS: 12(2002)4
pp 513539.)
(abstract)

Finite sumproduct logic (CockettSeely) (TAC 8(2001)5, pp 63  99)
(abstract)

Introduction to linear bicategories (CockettKoslowskiSeely)
(abstract)
(
"Lambekfest" MSCS:10(2000)2 pp 165203)

Feedback for linearly distributive categories: traces and fixpoints
(BluteCockettSeely)
(abstract) ("Bill(Lawvere)Fest", JPAA:154(2000) pp 2769.)

Linearly Distributive Functors (CockettSeely)
(abstract)
("BarrFest"
JPAA:143(1999) pp 155203.)
[Note change in terminology]

Weakly Distributive Categories
(CockettSeely) (JPAA 114(1997)2, pp 133173; Note:
This is the "corrected" version.)
(abstract)

Proof Theory for full intuitionistic linear logic, bilinear logic, and MIX
categories (CockettSeely) (TAC 3(1997)5, pp 85  131)
(abstract)

Categories for computation in context and unified logic
(BluteCockettSeely) (JPAA 116(1997), pp 4998)
(abstract)
(An earlier version is also available
(abstract))
 Natural
Deduction and Coherence for Weakly Distributive Categories
(BluteCockettSeelyTrimble) (JPAA 113(1996)3, pp 229296)
(abstract)
[BCST]

! and ?: Storage as Tensorial Strength
(BluteCockettSeely) (MSCS 6(1996)4, pp 313351)
(abstract)

Weakly Distributive Categories (CockettSeely) (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
Other papers
 Joachim
Lambek, FRSC, December 5, 1922  June 23, 2014 A tribute essay in
the Spring 2015 issue of Le Bulletin
(211), Centre de Recherches
Mathématiques (pp 1213).
[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 A0size poster]
 Editors'
note: bibliometrics and the curators of orthodoxy  Editorial
Board of MSCS. [Full text]
 Models,
Logics, and HigherDimensional 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
(BlutePanangadenSeely) (a corrected version of
MFPS'93
paper Springer LNCS 802)
(abstract)

A Logical Calculus for Polynomialtime Realizability
(CrossleyMathaiSeely, Methods of Logic in Comp Sci 1 (1994) 279298)
(abstract)

Category Theory 1991: Proceedings of the 1991 Summer Category Theory Meeting,
Montreal, Canada. (R.A.G. Seely, editor, CMS.)

Graded Multicategories of Polynomialtime 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 2categorical
framework. (RAG Seely, Proc. Symposium on Logic in Computer Science, 1987,
Computer Society of the IEEE, 6571.)
 Locally Cartesian closed categories and
type theory. (RAG Seely, Math. Proc. Cambridge Philos. Soc. 95 (1984), no. 1,
3348.)
 Hyperdoctrines, natural deduction, and the
Beck condition.
(RAG Seely, Zeitschrift f. math. Logik und Grundlagen d. Math. 29 (1983) 505542.)
 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
Maths and Category Theory Sites
Tools
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.; ClemensSeely,
K. 2021).
 Sediment
load and timing of sedimentation affect spore establishment in
Macrocystis pyrifera and Undaria pinnatifida
(Geange, Powell, ClemensSeely, A. Cárdenas, Marine Biology,
161(7): 15831592, July 2014)

Effects of Temperature on Hatching Time and Hatchling Proportions in a
Poecilogonous Population of Haminoea zelandiae
(Alternate link)
(ClemensSeely & Phillips,
Biol. Bull. 221: 189196, October 2011).
 Grammy
Nominees from McGill, 2016 (Check out Steinberg: Passion Week)

InfoCult/InfoSecte (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

Yeah^{3}(r.m.b.)

The Beatles in Canada
The Penrose Quilt (by
L.G. Clemens)
Other quilts
For comments or help, please contact
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)
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