Here are my papers, grouped by subject.
Size:
Spaces of extremal magnitude
(with Mark Meckes),
arXiv:2112.12889, 7 pages, 2021
|
The maximum entropy of a metric
space
(with Emily Roff),
arXiv:1908.11184; also Quarterly Journal of Mathematics 72 (2021), 1271–1309
|
Entropy modulo a prime,
arXiv:1903.06961; also Communications in Number Theory and Physics 15(2) (2021), 279–314; discussion
|
A short characterization of relative entropy,
arXiv:1712.04903; also Journal of
Mathematical Physics 60 (2019), Issue 2, 023302; discussion
|
Magnitude homology of enriched categories and metric spaces
(with Michael Shulman),
arXiv:1711.00802 (with major
rewrite in 2020); also Algebraic & Geometric
Topology 21 (2021), 2175–2221; discussion
|
The magnitude of a metric space: from category theory to geometric measure
theory (with Mark
Meckes),
arXiv:1606.00095; also in Nicola Gigli (ed.), Measure Theory in Non-Smooth
Spaces, de Gruyter Open, 2017
|
Maximizing diversity in biology and beyond
(with
Mark Meckes),
arXiv:1512.06314;
also Entropy 18
(2016), article 88
|
On the magnitude of a finite dimensional algebra,
(with Joseph Chuang and
Alastair King),
arXiv:1505.04281;
also Theory
and Applications of Categories 31 (2016), 63–72
|
The magnitude of a
graph, arXiv:1401.4623; also Mathematical Proceedings of the Cambridge
Philosophical Society 166 (2019), 247–264; discussions
(1, 2,
3)
|
Codensity and the ultrafilter monad,
arXiv:1209.3606; also Theory
and Applications of Categories 28 (2013), 332–370; discussions
(1,
2,
3,
4)
|
Notions of Möbius inversion,
arXiv:1201.0413;
also Bulletin of the Belgian Mathematical Society—Simon Stevin 19 (2012), 911–935;
discussion
|
Measuring
diversity: the importance of species similarity (with Christina Cobbold),
Ecology 93
(2012), 477–489
|
A characterization of entropy in terms of information loss (with
John Baez and
Tobias Fritz),
arXiv:1106.1791;
also Entropy 13
(2011), no. 11, 1945–1957;
discussion
|
A multiplicative characterization of the power means,
arXiv:1103.2574;
also Bulletin of the London Mathematical Society 44 (2012),
106–112;
discussion
|
The magnitude of metric spaces,
arXiv:1012.5857; also
Documenta Mathematica 18 (2013), 857–905; discussion
|
Integral geometry for the 1-norm,
arXiv:1012.5881;
also Advances in Applied Mathematics 49 (2012), 81–96;
discussion
|
A maximum entropy theorem with applications to the measurement of biodiversity, arXiv:0910.0906, 27 pages, 2009
|
On the asymptotic magnitude of subsets of Euclidean space (with Simon Willerton),
arXiv:0908.1582;
Geometriae
Dedicata 164 (2013), 287–310; discussion
|
The Euler characteristic of a category as the sum of a divergent
series (with Clemens Berger),
arXiv:0707.0835;
also Homology,
Homotopy and Applications 10(1) (2008), 41–51;
discussion
|
The Euler characteristic of a category,
math.CT/0610260; also Documenta
Mathematica 13 (2008), 21–49; nice
description here and discussion
here and here
|
Self-similarity and recursion:
A general theory of self-similarity,
arXiv:1010.4474;
also
Advances in
Mathematics 226 (2011), 2935–3017.
Supersedes the preprints 'A general theory of self-similarity I' and 'A
general theory of self-similarity II'
|
General self-similarity: an overview,
math.DS/0411343,
10 pages, 2004; also in Real
and Complex Singularities
(Proceedings of the Australian-Japanese Workshop, Sydney, 2005),
World Scientific (2007)
|
A general theory of self-similarity II: recognition,
math.DS/0411345,
28 pages, 2004. An updated version of this, merged with part I, is published
as 'A general theory of self-similarity' (above)
|
A general theory of self-similarity I,
math.DS/0411344,
49 pages, 2004. An updated version of this, merged with part II, is published
as 'A general theory of self-similarity' (above)
|
Objects of categories as complex numbers (with
Marcelo Fiore),
math.CT/0212377;
also
Advances in Mathematics
190 (2005), 264-277
|
An objective representation of the Gaussian integers (with
Marcelo Fiore),
math.RA/0211454;
also
Journal of Symbolic Computation
37 (2004), no. 6, 707-716
|
Category theory in algebra:
Higher category theory:
Weak ∞-categories via terminal coalgebras
(with Eugenia Cheng),
arXiv:1212.5853;
also Theory
and Applications of Categories 34 (2019),
no. 34, 1073–1133
|
A survey of definitions of n-category,
math.CT/0107188;
also
Theory and Applications of
Categories
10 (2002), no. 1, 1–70
|
Topology and higher-dimensional category theory: the rough idea,
math.CT/0106240,
15 pages, 2001
|
Operads in higher-dimensional category theory (PhD thesis),
math.CT/0011106; also
Theory and Applications of
Categories
12 (2004), no. 3, 73–194
|
Generalized enrichment of categories,
math.CT/0204279;
also
Journal of Pure and Applied Algebra 168 (2002),
391–406
|
fc-multicategories,
math.CT/9903004,
8 pages, 1999
|
Generalized enrichment for categories and multicategories,
math.CT/9901139,
79 pages, 1999
|
Basic bicategories,
math.CT/9810017,
11 pages, 1998
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Structures in higher-dimensional category theory,
math.CT/0109021,
81 pages, 1998
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General operads and multicategories,
math.CT/9810053,
35 pages, 1997
|
(Polished versions of most of the material in these unpublished papers can be
found in my book.)
Homotopy algebra:
Miscellaneous:
The eventual image,
arXiv:2210.00302, 39 pages, 2022
|
Isbell conjugacy and the reflexive completion (with Tom
Avery),
arXiv:2102.08290;
also Theory
and Applications of Categories 36 (2021), 306–347
|
A categorical derivation of Lebesgue integration, arXiv:2011.00412,
24 pages, 2020; also Journal of the London Mathematical Society, to
appear; discussions
(1, 2)
|
The probability that an operator is nilpotent,
arXiv:1912.12562;
also American Mathematical Monthly 128 (4) (2021), 371–375
|
The bijection between projective indecomposable and simple modules,
arXiv:1410.3671, 10 pages,
2014; also Bulletin of the Belgian Mathematical Society—Simon
Stevin 22 (2015), 725–735
|
Notes on commutation of limits and colimits (with Marie Bjerrum, Peter
Johnstone and Will Sawin),
arXiv:1409.7860, 5 pages,
2014;
also Theory
and Applications of Categories 30 (2015), 527–532
|
Rethinking set theory,
arXiv:1212.6543,
8 pages, 2012; also American Mathematical Monthly 121 (2014), no. 5, 403–415
|
An informal introduction to topos theory,
arXiv:1012.5647, 27 pages;
also
Publications of the
nLab 1 (2011), no. 1
|
Perfect numbers and groups,
math.GR/0104012,
12 pages, 1996ish; associated Sloane's integer sequence
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For other writing (reviews, magazine articles, blog posts, ...),
see Notes below.
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