Here are my papers, grouped by subject.
Size:
The maximum entropy of a metric
space
(with Emily Roff),
arXiv:1908.11184,
43 pages, 2019; Quarterly Journal of Mathematics, to appear

Entropy modulo a prime,
arXiv:1903.06961, 28 pages,
2019; Communications in Number Theory and Physics, to appear; discussion

A short characterization of relative entropy,
arXiv:1712.04903, 10 pages,
2017; 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, 32 pages,
2017 (with major rewrite in 2020); also Algebraic & Geometric Topology, to appear; discussion

The magnitude of a metric space: from category theory to geometric measure
theory (with Mark
Meckes),
arXiv:1606.00095, 32 pages,
2016; also in Nicola Gigli (ed.), Measure Theory in NonSmooth
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, 19
pages, 2014; 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 1norm,
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

Selfsimilarity and recursion:
A general theory of selfsimilarity,
arXiv:1010.4474;
also
Advances in
Mathematics 226 (2011), 2935–3017.
Supersedes the preprints 'A general theory of selfsimilarity I' and 'A
general theory of selfsimilarity II'

General selfsimilarity: an overview,
math.DS/0411343,
10 pages, 2004; also in Real
and Complex Singularities
(Proceedings of the AustralianJapanese Workshop, Sydney, 2005),
World Scientific (2007)

A general theory of selfsimilarity II: recognition,
math.DS/0411345,
28 pages, 2004. An updated version of this, merged with part I, is published
as 'A general theory of selfsimilarity' (above)

A general theory of selfsimilarity I,
math.DS/0411344,
49 pages, 2004. An updated version of this, merged with part II, is published
as 'A general theory of selfsimilarity' (above)

Objects of categories as complex numbers (with
Marcelo Fiore),
math.CT/0212377;
also
Advances in Mathematics
190 (2005), 264277

An objective representation of the Gaussian integers (with
Marcelo Fiore),
math.RA/0211454;
also
Journal of Symbolic Computation
37 (2004), no. 6, 707716

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 ncategory,
math.CT/0107188;
also
Theory and Applications of
Categories
10 (2002), no. 1, 1–70

Topology and higherdimensional category theory: the rough idea,
math.CT/0106240,
15 pages, 2001

Operads in higherdimensional 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

fcmulticategories,
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

Structures in higherdimensional category theory,
math.CT/0109021,
81 pages, 1998

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:
Isbell conjugacy and the reflexive completion (with Tom
Avery),
arXiv:2102.08290;
also Theory
and Applications of Categories 36 (2021), 306–347

The categorical origins of Lebesgue integration, arXiv:2011.00412,
23 pages, 2020; 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

For other writing (reviews, magazine articles, blog posts, ...),
see Notes below.
