Publications
of Ross Street
0. PhD Thesis: Homotopy Classification of Filtered
Complexes, University of Sydney, August 1968.
1. (with E. Dubuc) Dinatural transformations, Lecture
Notes in Math. 137 (1970) 126-137; MR43#313.
2. Projective diagrams of interlocking sequences, Illinois
J. Math. 15 (1971) 429-441; MR43#4881.
3. The formal theory of monads, J. Pure Appl.
Algebra 2 (1972) 149-168; MR45#8701.
4. Two constructions on lax functors, Cahiers
topologie et gŽomŽtrie diffŽrentielle 13 (1972) 217-264;
MR50#436.
5. Homotopy classification of filtered complexes, J.
Australian Math. Soc. 15 (1973) 298-318;
MR49#5135.
6. (with R.F.C. Walters) The comprehensive
factorization of a functor, Bulletin American Math. Soc. 79
(1973) 936-941; MR49#10753.
7. (with G.M. Kelly) Review of the elements of
2-categories, Lecture Notes in Math. 420
(1974) 75-103; MR50#10010.
8. Fibrations and Yoneda's lemma in a 2-category, Lecture
Notes in Math. 420 (1974) 104-133; MR53#585.
9. Elementary cosmoi I, Lecture Notes in Math. 420
(1974) 134-180; MR50#7290.
10. Limits indexed by category-valued 2-functors, J.
Pure Appl. Algebra 8 (1976) 149-181;
MR53#5695.
11. Internally complete 2-categories, Notices
American Math. Soc. 23#5 (Aug.1976)
Abstract 737-18-7.
12. (with R.F.C. Walters) Yoneda structures on
2-categories, J. Algebra 50 (1978) 350-379;
MR57#3214.
13. Cosmoi of internal categories, Transactions
American Math. Soc. 258 (1980) 271-318;
MR82a:18007.
14. Fibrations in bicategories, Cahiers topologie
et gŽomŽtrie diffŽrentielle 21 (1980) 111-160;
MR81f:18028.
15. (with W. Tholen, M. Wischnewsky, and H. Wolff)
Semi-topological functors III: lifting of monads and adjoint functors, J.
Pure Appl. Algebra 16 (1980) 299-314;
MR81g:18003.
16. Notions of topos, Bulletin Australian Math.
Soc. 23 (1981) 199-208; MR83a:18014.
17. Conspectus of variable categories, J. Pure
Appl. Algebra 21 (1981) 307-338; MR84i:18006.
18. [see 85] Cauchy characterization of enriched
categories, Rendiconti del Seminario Matematico e Fisico di Milano 51
(1981) 217-233; MR85e:18006; pdf
19. Two dimensional sheaf theory, J. Pure Appl.
Algebra 23 (1982) 251-270; MR83d:18014.
20. Characterization of bicategories of stacks, Lecture
Notes in Math. 962 (1982) 282-291; MR84d:18006.
21. Enriched categories and cohomology, Quaestiones
Math. 6 (1983) 265-283; MR85e:18007.
22. (with R. Betti, A. Carboni, and R. Walters)
Variation through enrichment, J. Pure Appl. Algebra 29
(1983) 109-127; MR85e:18005.
23. Absolute colimits in enriched categories, Cahiers
topologie et gŽomŽtrie diffŽrentielle 24 (1983) 377- 379;
MR85i:18001.
24. The family approach to total cocompleteness and
toposes, Transactions American Math. Soc. 284
(1984) 355-369; MR85f:18003.
25. Homotopy classification by diagrams of
interlocking sequences, Math. Colloquium University of Cape Town 13
(1984) 83-120; MR86i:55025; large pdf file of 8MB.
26. (with A. Carboni and S. Kasangian) Bicategories of
spans and relations, J. Pure Appl. Algebra 33
(1984) 259-267; MR86f:18013.
27. (with A. Carboni) Order ideals in categories, Pacific
J. Math. 124 (1986) 275-288; MR88e:18005.
28. (with S. Schanuel) The free adjunction, Cahiers
topologie et gŽomŽtrie diffŽrentielle catŽgoriques 27 (1986) 81-83; MR87f: 18005.
29. (with B.J. Day) Categories in which all strong
generators are dense, J. Pure Appl. Algebra 43
(1986) 235-242; MR88m:18013.
30. The algebra of oriented simplexes, J. Pure Appl.
Algebra 49 (1987) 283-335; MR89a:18019.
(2.2Mb pdf; see [52]
for a correction).
31. Correction to "Fibrations in
bicategories", Cahiers topologie et gŽomŽtrie diffŽrentielle
catŽgoriques 28 (1987) 53-56; MR88i: 18004.
32. (with D. Schumacher) Some parametrized categorical
concepts, Communications in Algebra 16
(1988) 2313-2347; MR89k:18001.
33. Fillers for nerves, Lecture Notes in Math. 1348
(1988) 337-341; MR89m:18011.
34. (with B.J. Day) Localisation of locally
presentable categories, J. Pure Appl. Algebra 58
(1989) 227- 233; MR90g:18012.
35. (with G.J. Bird, G.M. Kelly, and A.J. Power)
Flexible limits for 2-categories, J. Pure Appl. Algebra 61
(1989) 1-27; MR91a:18009.
36. (with B.J. Day) Localisation of locally
presentable categories II, J. Pure Appl. Algebra 63
(1990) 225-229; MR91h:18007.
37. (with A. Joyal) The geometry of tensor calculus I,
Advances in Math. 88
(1991) 55-112; MR92d:18011.
38. (with A. Joyal) Tortile Yang-Baxter operators in
tensor categories, J. Pure Appl. Algebra 71
(1991) 43-51; MR92e:18006.
39. Quantum Groups : an entrŽe to modern algebra
(Notes from a Graduate Lecture Course March-June 1990; nearly all available as html or ps).
40. (with A. Joyal) An introduction to Tannaka
duality and quantum groups; Part II of Category Theory,
Proceedings, Como 1990 (Editors A. Carboni, M.C. Pedicchio and G. Rosolini) Lecture
Notes in Math. 1488 (Springer-Verlag Berlin,
Heidelberg 1991) 411-492; MR93f:18015.
41. Parity complexes, Cahiers topologie et
gŽomŽtrie diffŽrentielle catŽgoriques 32 (1991) 315-343;
MR93f:18014.
42. (with A. Joyal) Pullbacks equivalent to
pseudopullbacks, Cahiers topologie et gŽomŽtrie diffŽrentielle catŽgoriques 34 (1993) 153-156;
MR94a:18004.
43. (with G. Janelidze and D. Schumacher) Galois
theory in variable categories, Applied Categorical Structures 1
(1993) 103-110; MR94k:18011.
44. (with A. Joyal) Braided tensor categories, Advances in Math. 102
(1993) 20-78; MR94m:18008; for earlier version see "Other widely circulated output ix"
below.
45. Categorical structures, Handbook of Algebra Volume
1 (editor M. Hazewinkel; Elsevier Science, Amsterdam 1996; ISBN 0 444
82212 7) 529-577.
46. (with A. Carboni, S. Johnson and D. Verity)
Modulated bicategories, J. Pure Appl. Algebra 94
(1994) 229-282; MR96f:18008.
47. (with R. Gordon and A.J. Power) Coherence for
tricategories, Memoirs of the American Math. Society 117
(1995) Number 558 (ISBN 0-8218-0344-1); MR96j:18002.
48. Higher categories, strings, cubes and simplex
equations, Applied Categorical Structures 3
(1995) 29- 77 & 303; MR96b:18009.
49. (with A. Joyal) The category of representations of
the general linear groups over a finite field, J. Algebra 176 (3)
(1995) 908-946; MR96k:20082
50. Ideals, radicals, and structure of additive
categories, Applied Categorical Structures 3
(1995) 139-149; MR96e:18003.
51. (with A. Joyal and D. Verity) Traced monoidal
categories, Mathematical Proceedings of the Cambridge Philosophical Society 119 (3)
(1996) 425-446; MR96m:18014.
52. Parity complexes: corrigenda, Cahiers topologie
et gŽomŽtrie diffŽrentielle catŽgoriques 35 (1994) 359-361; MR95j:18005.
53. (with A. Joyal) The geometry of tensor calculus II
(draft document,
also see (xii) below).
54. (with D. Verity) Surface diagrams for
tricategories; superseded by
M. McIntyre and
T. Trimble, The geometry of Gray-categories, Advances in Math. (to
appear).
55. (with B. Day) Kan extensions along promonoidal
functors, Theory and Applications
of Categories 1 (4) (1995)
72-78; MR96a:18003 <ftp://ftp.tac.mta.ca/pub/tac/volumes/1995/n4/v1n4.{dvi,ps}>
56. (with P. Freyd) On the size of categories, Theory and Applications
of Categories 1 (9) (1995)
174-178 <ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n9/v1n9.{dvi,ps}>
or <http://www.tac.mta.ca/tac/> ; MR96m:18004.
57. Low-dimensional topology and higher-order
categories, Proceedings of CT95, Halifax,
July 9-15 1995; pdf version.
58. Fusion operators and cocycloids in monoidal
categories, Applied Categorical Structures 6 (2)
(Special Issue on "Quantum Groups, Hopf Algebras and Category
Theory", ed. A. Verschoren, 1998) 177-191; MR99d:18008.
59. Descent theory (notes of three lectures presented
at Oberwolfach,
September 1995); pdf version.
60. (with B.J. Day) Monoidal bicategories and Hopf
algebroids, Advances in Math. 129
(1997) 99-157; MR99f:18013.
61. (with Renato Betti and Dietmar Schumacher)
Factorizations in bicategories (preprint 1995; submitted; under revision).
62. (with P.J. Freyd, P.W. O'Hearn, A.J. Power, M.
Takeyama, and R.D. Tennent) Bireflectivity, Theoretical Computer
Science 228 (1-2)
(1999) 49-76; MR2000i:68110.
63. The quantum double and related constructions, J.
Pure Appl. Algebra 132 (1998) 195-206;
MR99e:16054.
64. The role of Michael Batanin's
monoidal globular categories, in:
"Higher Category Theory" (editors E. Getzler and M. Kapranov) Contemporary
Mathematics 230 (A.M.S. 1998) 99-116; MR
2000a:18006.
65. Parenthetic remarks (in preparation; pdf).
66. (with M. Batanin) The universal property of
the multitude of trees, J. Pure Appl. Algebra 154
(2000) 3-13; MR2001f:18014.
67. (with G. Janelidze) Galois theory in symmetric
monoidal categories, Macquarie Mathematics Report 98/235
(April 1998); preliminary announcement in Seminarberichte
aus dem Fachbereich Mathematik, Band 63,
Teil 3 (1998) 365-375; Journal of Algebra 220
(1999) 174-187; MR2000h:18017.
68. Braids among the groups Seminarberichte
aus dem Fachbereich Mathematik, Band 63,
Teil 5 (1998) 699-703.
69. The petit topos of globular sets, J. Pure Appl. Algebra 154
(2000) 299-315; MR2001f:18008.
70. (with G.M. Kelly, A. Labella and V. Schmitt)
Categories enriched on two sides, J. Pure Appl. Algebra 168
(1) (8 March 2002) 53-98; MR2003f:18006 pdf.
71. (with S. Lack) The formal theory of monads II, J.
Pure Appl. Algebra 175 (1-3)
(2002) 243-265; MR2003m:18007 ps.gz.
72. (with B.J. Day) Lax monoids, pseudo-operads, and
convolution, in: "Diagrammatic Morphisms and Applications", Contemporary
Mathematics 318 (AMS; ISBN 0-8218-2794-4; April
2003) 75-96; MR2004c:18011; pdf.
73. (with J. Bichon) Militaru's D-equation in monoidal
categories, Applied Categorical Structures 11
(2003) 337-357; MR2004f:18011; ps.gz.
74. Functorial calculus in monoidal bicategories, Applied
Categorical Structures 11 (2003) 219-227;
MR2004f:18010; pdf.
75. (with B.J. Day and P. McCrudden) Dualizations and
antipodes, Applied Categorical Structures 11
(2003) 229-260; MR2004b:18013; pdf.
76. Weak omega-categories, in: "Diagrammatic
Morphisms and Applications", Contemporary Mathematics 318
(AMS; ISBN 0-8218-2794-4; April 2003) 207-213; MR 2004c:18008; pdf.
77. (with B.J. Day) Abstract substitution in enriched
categories, J. Pure Appl. Algebra 179 (2003)
49-63; MR2004d:18008; pdf.
78. (with A. Davydov) Roots of unity as a Lie algebra,
Georgian Mathematical Journal 9(4)
(2002) 683-690; MR2004c:18010 pdf.
79. (with B.J. Day) Quantum categories, star autonomy,
and quantum groupoids, in "Galois Theory, Hopf Algebras, and Semiabelian
Categories", Fields Institute Communications 43
(American Math. Soc. 2004) 187-226 (preprint pdf or math.CT/0301209).
80. Categorical and combinatorial aspects of descent
theory, Applied Categorical Structures 12
(2004) 537-576 (preprint at pdf and math.CT/0303175;
also see the supplementary expository article [o] below);
MR2005h:18022.
81. The monoidal centre as a limit, Theory and
Applications of Categories 13 (ed. G.
Janelidze, S. Lack, F.W. Lawvere, E.M. Vitale and R.J. Wood: volume dedicated
to Aurelio Carboni for his 60th birthday; 2004) 184-190 (old preprint pdf or
even older version at math.CT/0304053);
MR2005h:18027.
82. (with R. Buchweitz and A. Davydov) The
Gerstenhaber homotopy in a monoidal bicategory (in preparation).
83. Frobenius monads and pseudomonoids, J. Math.
Physics 45(10) (October 2004)
3930-3948 (old preprint pdf);
MR2005h:18026.
84. Monoidal actions, enriched categories, and
convolution (in preparation).
85. [see 18] Cauchy characterization of enriched
categories, Reprints in Theory and
Applications of Categories 4 (2004) 1-16.
86. An Australian conspectus of higher categories (to
appear in the proceedings of the 2004 Summer Program: n-Categories: Foundations and Applications,
1-18 June 2004 at the IMA of the University of
Minnesota, Minneapolis); available at pdf.
87. (with Brian
Day and Elango Panchadcharam) Lax braidings and the lax centre, in "Hopf
Algebras and Generalizations" Contemporary Mathematics 441 (2007;
pdf; details)
1-17.
88. [see 21] Enriched categories and cohomology with
author commentary, Reprints in Theory and
Applications of Categories 14 (2005) 1-18.
89. (with Brian Day) Centres of monoidal categories of
functors, in "Categories in Algebra, Geometry and Mathematical
Physics", Contemporary Mathematics 431
(2007) 187-202 (details).
90. [see 39] Quantum Groups: a path to
current algebra, Australian Math. Society Lecture
Series 19 (Cambridge University Press; 18
January 2007; ISBN-978-0-521-69524-4).
91. (with Brian Day and Elango Panchadcharam) On
centres and lax centres for promonoidal categories, Colloque International
"Charles Ehresmann : 100 ans UniversitŽ de Picardie Jules Verne ˆ Amiens
7-8-9 Octobre 2005" <pdf>.
92. (with Eduardo Dubuc) A construction of 2-filtered
bicolimits of categories, Cahiers de topologie et gŽomŽtrie diffŽrentielle
catŽgoriques 47(2) (2006) 83-106 <pdf>.
93. (with Elango Panchadcharam) Mackey functors on
compact closed categories, Journal of Homotopy and Related Structures 2(2) (2007)
261–293; http://arxiv.org/abs/0706.2922.
94. (with Elango Panchadcharam) Pullback and finite
coproduct preserving functors between categories of permutation
representations, Theory and Applications of Categories 16(28)
(2006) 771-784 <pdf>.
95. (with Elango Panchadcharam) Pullback and finite
coproduct preserving functors between categories of permutation
representations: corrigendum and addendum, Theory and Applications of
Categories, 18(5) (2007) 151-156
<pdf>.
96. (with Craig Pastro) Weak Hopf monoids in braided
monoidal categories (submitted; http://arxiv.org/abs/0801.4067).
97. (with Craig Pastro) Closed categories,
star-autonomy, and monoidal comonads, Journal of Algebra (to
appear in special volume for the 60th birthday of Gus Lehrer; http://arxiv.org/abs/0712.0418)
98. (with Craig Pastro) Doubles for monoidal
categories, Theory and Applications of Categories, 21(4)
(2008) 61-75; pdf
(also http://arxiv.org/abs/0711.1859).
99. (with Ignacio Lopez-Franco and Richard Wood) Duals
invert (in preparation).
100. (with Ronald Brown) Universal coverings of tensor
products of crossed complexes and cubical omega-groupoids (in preparation).
Volumes Edited
(with George Janelidze, John MacDonald and Walter
Tholen) Proceedings of CT2004 at UBC (Vancouver), Theory and Applications of
Categories 15.
(with Aurelio Carboni and George Janelidze) Special
Volume celebrating the 70th birthday of Professor Max Kelly, Journal
of Pure and Applied Algebra 175(1-3) (8 November
2002).
Volume
Dedicated
ÒCategories in Algebra, Geometry and Mathematical
PhysicsÓ, Conference and Workshop in honor of Ross StreetÕs 60th
Birthday, Macquarie University 11-16 July 2005 and Australian National
University 18-21 July 2005; edited by Alexei Davydov, Michael Batanin, Michael
Johnson, Stephen Lack and Amnon Neeman; Contemporary Mathematics 431
(American Math. Society, 2007).
Expository Articles
a. Geometry using painting, Parabola 10 #2
(1974) 8-13.
b. Numbers from space, Reflections 7
(Math. Assoc. of NSW, 1982) 8-10.
c. An efficient construction of the real numbers, Gazette
Australian Math. Soc. 12 (1985) 57-58.
Click here for a full
version (jointly with Vacation Scholars James Douglas, Rony Kirollos, Ben
Odgers and Nguyen Hanh Vo; February 2004) including the original article. There
is also the older September 2003 update.
d. The mathematics of knots, Reflections 21
(4) (Math. Assoc. of NSW, 1996) 12-21 .
e. Bicategories and 2-categories, Encyclopaedia of
Mathematics, Supplement II (ed. M. Hazewinkel; Kluwer Academic,
2000) 65-67.
f. Higher-dimensional categories; n-categories, Encyclopaedia
of Mathematics, Supplement II (ed. M. Hazewinkel; Kluwer Academic,
2000) 254-257.
g. Consequences of splitting idempotents (November
1996, notes; pdf)
h. Branches of higher
dimensional algebra, Talk at Aust Math Soc Conference at
the University of Sydney (30 September 1998)
i. Rationals, reals, complexes! What next? (Blakers
Lecture, National Mathematics Summer School, 18 January 1999; it is a talk
about quaternions)
j. Trees, permutations and the tangent function, Reflections 27
(2) (Math. Assoc. of NSW, May 2002) 19-23; pdf and math.HO/0303267.
k. Powerful functors; pdf
l. The 3-cocycle condition; pdf
m. Formal representation theory, Invited talk at the
Fields Institute (Toronto, Canada, September 2002); audio and lecture notes.
n. Lack's lemma on comma objects.
o. Lecture at ICIAM 2003 (11 July 2003)
"Categorical and combinatorial aspects of descent theory", 2003ICIAM.pdf (while
this is intended to be self-contained, it is supplementary to [80] above).
p. Monoidal categories for the combinatorics of group
representations; pdf
q. Frobenius algebras and
monoidal categories, Lecture at the Annual Meeting of the
Australian Math. Soc. (29 September 2004).
Book Reviews
I. Review of: J.W. Gray, Formal Category Theory :
Adjointness for 2-Categories (Lecture Notes in Math. 391,
Springer 1974); in Mathematical Reviews 51#8207 (April
1976) 1153.
II. Review of: Kirill Mackenzie, Lie Groupoids and
Lie Algebroids in Differential Geometry (London Math.
Soc. Lecture Note Series No.124, Cambridge University Press
1987); in Gazette Australian Math. Soc. 16#3
(June 1989) 66-68.
III. Review of: Colin McLarty, Elementary
Categories, Elementary Toposes (Oxford University Press 1992);
in Zentralblatt fŸr Mathematik 762 (12)
(1993) #18001.
IV. Review of: Robert Gordon, G-Categories
(Memoirs Amer. Math. Soc. 101 (1993) #482); in Mathematical
Reviews MR# 93f:18003.
V. Review of: Frederick Chong and Ronald J. Andrews, A
View of Mathematics: Big Picture Plus Close-ups (The
Mathematical Association of New South Wales, March 1995), Gazette Australian
Math. Soc. 23 (5) (1996) 214-215.
VI. Review of: David N. Yetter, Functorial knot
theory: Categories of tangles, coherence, categorical deformations, and
topological invariants, (Series on Knots and Everything 26, World
Scientific, Singapore, 2001): in Bulletin of the London Mathematical Society
35 (2003) 137-139.
VII. Review of: Tom Leinster, Higher Operads,
Higher Categories, (London Math. Soc. Lecture Note Series 298,
Cambridge University Press 2004); in Mathematical Reviews MR2094071.
VIII. Review of: Peter T. Johnstone, Sketches of an
elephant. A topos theory compendium. I and II. (Oxford Logic
Guides 44; Oxford Science Publications. Oxford: Clarendon Press, 2002); in Zentralblatt
fŸr Mathematik Zbl 1071.18002.
Speech
In celebration of Professor Chong's eightieth
birthday, Reflections 24 (2) (May, 1999)
2-3.
Obituaries
Professor Frederick Chong, Gazette Austral. Math.
Society 26 #4 (October 1999) 211-213.
Professor G. Maxwell Kelly, ÒPolymath revelled in the
mystery of numbersÓ Sydney Morning Herald (Timelines 11
April 2007).
Professor
G. Maxwell Kelly, Gazette Austral. Math. Society 34
#2 (May 2007) 94-96.
(with W. Chen and K. Matthews) Dr
Peter Pleasants, Gazette Austral. Math. Society 35
#3 (July 2008) 162-165.
Other widely circulated output
i. The universal property of the representation functor
(1972).
ii. (editor, with G.M. Kelly) Abstracts of the
Sydney Category Seminar 1972. (First printing at Univ. of NSW; second
at Macquarie University).
iii. The calculus of modules (1976).
iv. Survey of topos theory (1978).
v. The comprehensive construction of free colimits, Macquarie
Math. Reports 79000 (1979).
vi. One-dimensional non-abelian cohomology, Macquarie
Math. Reports 810024 (1981).
vii. An unpublished theorem of P.J. Freyd and R.
Street discussed with attribution in [G.M. Kelly and V. Koubek, The large
limits that all good categories admit, J. Pure Appl. Algebra 22
(1981) 253-263].
viii. (with B.J. Day) An additive Giraud theorem
(1984).
ix. (with A. Joyal) Braided monoidal categories, Macquarie Math Reports 860081
(1986); Macquarie Math Reports 850067
(1985).
x. Gray's tensor product
of 2-categories (February 1988).
xi. A construction of the Azumaya complex, on page 116
of "The Azumaya complex of a commutative ring" by J.W. Duskin, Lecture
Notes in Math. 1348 (1988)107-117; MR90c:13003.
xii. (with A. Joyal) Planar diagrams and
tensor algebra (1988).
xiii. Higher descent structures, Geometric and Logical
Aspects of Descent Theory 17.09.-23.09.1995 (Tagungsbericht 38/1995,
Mathematisches Forschungsinstitut Oberwolfach).
Other material.
A. (with S. Eilenberg) Rewrite systems, algebraic
structures, and higher-order categories (handwritten manuscripts).
B. (with G.J. Bird, G.M. Kelly and A.J. Power)
Explicit formulas for the strict reflections of pseudo and lax natural
transformations.
C. The Tannakian adjunction.