Ross Street

Ross Howard Street (29 September 1945, Sydney –) is an Australian mathematician specialising in category theory. He did his undergraduate and postgraduate study at the University of Sydney, where his dissertation advisor was Max Kelly. He is an emeritus professor of mathematics at Macquarie University, a fellow of the Australian Mathematical Society (1995), and was elected Fellow of the Australian Academy of Science in 1989.He was awarded the Edgeworth David Medal of the Royal Society of New South Wales in 1977, and the Australian Mathematical Society's George Szekeres Medal in 2012.

An incomplete list. Some closely related papers by other authors are also included. In the following "SLNM" stands for Springer Lecture Notes in Mathematics, while the titles of the four journals most frequently publishing research on categories are abbreviated as follows: JPAA = Journal of Pure and Applied Algebra, TAC = Theory and Applications of Categories, ACS = Applied Categorical Structures, CTGDC = Cahiers de Topologie et Géométrie Différentielle Catégoriques (Volume XXV (1984) and later), CTGD = Cahiers de Topologie et Géométrie Différentielle (Volume XXIV (1983) and earlier). For a more complete list, see the list at Street's website, from which this list was derived. Some closely related or specialized items are listed not by date of publication, but by their topic.

1970

• Dubuc, Eduardo; Street, Ross (1970). "Dinatural transformations". Reports of the Midwest Category Seminar IV. Lecture Notes in Mathematics. 137. pp. 126–137. doi:10.1007/BFb0060443. ISBN 978-3-540-04926-5. MR 0274550.
• Street, Ross (1972). "Two constructions on lax functors". CTGD. 13 (3): 217–264. MR 0347936.
• Bourn, Dominique (1973). "Natural anadeses and catadeses". CTGD. 14 (4): 371–415. MR 0354808. Cf. Street, "Two constructions on lax functors".
• Street, Ross; Walters, R.F.C. (1973). "The comprehensive factorization of a functor". Bull. Amer. Math. Soc. 79 (5): 936–941. doi:10.1090/S0002-9904-1973-13268-9. MR 0346027.
• Kelly, G. M.; Street, Ross (1974). "Review of the elements of 2-categories". Category Seminar (Proceedings Sydney Category Theory Seminar 1972/1973). Lecture Notes in Mathematics. 420. pp. 75–103. doi:10.1007/BFb0063101. ISBN 978-3-540-06966-9. MR 0357542.
• Street, Ross (1974). "Fibrations and Yoneda's lemma in a 2-category". Category Seminar (Proceedings Sydney Category Theory Seminar 1972/1973). Lecture Notes in Mathematics. 420. pp. 104–133. doi:10.1007/BFb0063102. ISBN 978-3-540-06966-9. MR 0396723. See also: Kock, Anders (2013-12-05). "Fibrations as Eilenberg-Moore algebras". pp. 1–24. arXiv:1312.1608 [math.CT]. Kock writes: "Street was probably the first to observe that opfibrations could be described as pseudo-algebras for a KZ monad [also known as lax-idempotent 2-monad]; in fact, in [F&YL], p. 118, he uses this description as his definition of the notion of opfibration, so therefore, no proof is given. Also, loc.cit. gives no proof of the fact that split opfibrations then are the strict algebras. So in this sense, Section 6 of the present article only supplements loc.cit. by providing elementary proofs of these facts."
• Street, Ross (1974). "Elementary cosmoi I". Category Seminar (Proceedings Sydney Category Theory Seminar 1972/1973). Lecture Notes in Mathematics. 420. pp. 134–180. doi:10.1007/BFb0063103. ISBN 978-3-540-06966-9. MR 0354813.
• Street, Ross (1976). "Limits indexed by category-valued 2-functors". JPAA. 8 (2): 149–181. doi:10.1016/0022-4049(76)90013-X. MR 0401868.
• Street, Ross; Walters, Robert (1978). "Yoneda structures on 2-categories". J. Algebra. 50 (2): 360–379. doi:10.1016/0021-8693(78)90160-6. MR 0463261.

1980

• Street, Ross (1980). "Cosmoi of internal categories". Trans. Amer. Math. Soc. 258 (2): 278–318. doi:10.1090/S0002-9947-1980-0558176-3. MR 0558176.
• Street, Ross (1980). "Fibrations in bicategories". CTGD. 21 (2): 111–160. MR 0574662., followed in 1987 by "Correction [and addendum] to Fibrations in bicategories". CTGDC. 28 (1): 53–56. 1987. MR 0903151. This paper discusses relations between ${\displaystyle {\cal {V}}}$-bimodules and two-sided fibrations and cofibrations in ${\displaystyle {\cal {V}}}$-Cat: "The ${\displaystyle {\cal {V}}}$-modules turn out to amount to the bicodiscrete cofibrations in ${\displaystyle {\cal {V}}}$-Cat." --- Closely related to these constructions is: Kasangian, S.; Kelly, G. M.; Rossi, F. (1983). "Cofibrations and the realization of non-deterministic automata". CTGD. 24 (1): 23–46. MR 0702718.
• Street, Ross; Tholen, Walter; Wischnewsky, Manfred; Wolff, Harvey (1980). "Semi-topological functors III: lifting of monads and adjoint functors". JPAA. 16 (3): 299–314. doi:10.1016/0022-4049(80)90035-3. MR 0558494.
• Street, Ross (1981). "Notions of topos". Bull. Austral. Math. Soc. 23 (2): 198–208. doi:10.1017/S000497270000705X. MR 0617062.
• Street, Ross (1981). "Conspectus of variable categories". JPAA. 21 (3): 307–338. doi:10.1016/0022-4049(81)90021-9. MR 0617138.
• Street, Ross (1981). "Cauchy characterization of enriched categories". Rendiconti del Seminario Matematico e Fisico di Milano. 51: 217–233. CiteSeerX 10.1.1.178.9997. doi:10.1007/BF02924823. MR 0708046. Republished as Street, Ross (2004). "Cauchy characterization of enriched categories". Reprints in Theory and Applications of Categories. 4: 1–16.
• Street, Ross (1982). "Two-dimensional sheaf theory". JPAA. 23 (3): 251–270. doi:10.1016/0022-4049(82)90101-3. MR 0644277.
• Street, Ross (1982). "Characterization of bicategories of stacks". Category Theory: Applications to Algebra, Logic and Topology. Proceedings of the International Conference Held at Gummersbach, July 6-10, 1981. Lecture Notes in Mathematics. 962. pp. 282–291. doi:10.1007/BFb0066878. ISBN 978-3-540-11961-6. MR 0682967.
• Street, Ross (1983). "Enriched categories and cohomology". Quaestiones Mathematicae. 6 (1–3): 265–283. CiteSeerX 10.1.1.144.5858. doi:10.1080/16073606.1983.9632304. MR 0700252. Republished as: Street, Ross (2005). "Enriched categories and cohomology with author commentary". Reprints in Theory and Applications of Categories. 14: 1–18.
• Betti, Renato; Carboni, Aurelio; Street, Ross; Walters, Robert (1983). "Variation through enrichment". JPAA. 29 (2): 109–127. doi:10.1016/0022-4049(83)90100-7. MR 0707614. Compare: Gordon, R.; Power, A. J. (1997). "Enrichment through variation". JPAA. 120 (2): 167–184. doi:10.1016/S0022-4049(97)00070-4.
• Street, Ross (1983). "Absolute colimits in enriched categories". CTGD. 24 (4): 377–379. MR 0749468.
• Street, Ross (1984). "The family approach to total cocompleteness and toposes". Trans. Amer. Math. Soc. 284: 355–369. doi:10.1090/S0002-9947-1984-0742429-3. MR 0742429.
• Carboni, Aurelio; Kasangian, Stefano; Street, Ross (1984). "Bicategories of spans and relations". JPAA. 33 (3): 259–267. doi:10.1016/0022-4049(84)90061-6. MR 0761632.
• Carboni, Aurelio; Street, Ross (1986). "Order ideals in categories". Pacific J. Math. 124 (2): 275–288. doi:10.2140/pjm.1986.124.275. MR 0856163.
• Street, Ross; Schanuel, Stephen (1986). "The free adjunction". CTGDC. 27 (1): 81–83. MR 0845410.
• Street, Ross (1986). "Categories in which all strong generators are dense". JPAA. 43 (3): 235–242. doi:10.1016/0022-4049(86)90065-4. MR 0868984.
• Street, Ross (1987). "The algebra of oriented simplexes". JPAA. 49 (3): 283–335. doi:10.1016/0022-4049(87)90137-X. MR 0920944.
• Schumacher, Dietmar; Street, Ross (1988). "Some parametrized categorical concepts". Communications in Algebra. 16 (11): 2313–2347. doi:10.1080/00927878808823693. MR 0962317.
• Street, Ross (1988). "Fillers for nerves". Categorical Algebra and its Applications : Proceedings of a Conference, held in Louvain-La-Neuve, Belgium, July 26 – August 1, 1987. Lecture Notes in Mathematics. 1348. pp. 337–341. doi:10.1007/BFb0081370. ISBN 978-3-540-50362-0. MR 0975981.
• Day, Brian; Street, Ross (1989). "Localisation of locally presentable categories". JPAA. 58 (3): 227–233. doi:10.1016/0022-4049(89)90038-8.
• Bird, G. J.; Kelly, G. M.; Power, A. J.; Street, R. H. (1989). "Flexible limits for 2-categories". JPAA. 61 (1): 1–27. doi:10.1016/0022-4049(89)90065-0. MR 1023741.

1990

• Day, Brian; Street, Ross (1990). "Localisations of locally presentable categories II". JPAA. 63 (3): 225–229. doi:10.1016/0022-4049(90)90068-S. MR 1047582.
• Joyal, André; Street, Ross (1991). "The geometry of tensor calculus, I". Advances in Mathematics. 88 (1): 55–112. doi:10.1016/0001-8708(91)90003-P. MR 1113284.
• Joyal, André; Street, Ross (1991). "Tortile Yang-Baxter operators in tensor categories". JPAA. 71 (1): 43–51. doi:10.1016/0022-4049(91)90039-5. MR 1107651.
• Joyal, André; Street, Ross (1991). "An introduction to Tannaka duality and quantum groups". Category Theory : Proceedings of the International Conference held in Como, Italy, July 22–28, 1990. Lecture Notes in Mathematics. 1488. pp. 413–492. doi:10.1007/BFb0084235. ISBN 978-3-540-54706-8. MR 1173027.
• Street, Ross (1991). "Parity complexes". CTGDC. 32 (4): 315–343. MR 1165827. "Parity complexes are a new combinatorial structure introduced here in order to provide a uniform treatment of the diagrams in all dimensions that appear in descent theory and in the theory of homotopy types." See also: Street, Ross (1994). "Parity complexes : corrigenda". CTGDC. 35 (4): 359–361. MR 1307269.
• Joyal, André; Street, Ross (1993). "Pullbacks equivalent to pseudopullbacks". CTGDC. 34 (2): 153–156. MR 0210112.
• Janelidze, George; Schumacher, Dietmar; Street, Ross (1993). "Galois theory in variable categories". ACS. 1 (1): 103–110. doi:10.1007/BF00872989. MR 1245796.
• Joyal, André; Street, Ross (1993). "Braided tensor categories". Advances in Mathematics. 102 (1): 20–78. doi:10.1006/aima.1993.1055. MR 1250465.
• Carboni, Aurelio; Johnson, Scott; Street, Ross; Verity, Dominic (1994). "Modulated bicategories". JPAA. 94 (3): 229–282. doi:10.1016/0022-4049(94)90009-4. MR 1285544.
• Gordon, R.; Power, A. J.; Street, Ross (1995). Coherence for tricategories. Memoirs of the American Mathematical Society. 558. pp. 1–81. ISBN 978-0-8218-0344-8. MR 1261589.
• Street, Ross (1995). "Higher categories, strings, cubes and simplex equations". ACS. 3 (1): 29–77. doi:10.1007/BF00872948. MR 1320574.
• Joyal, André; Street, Ross (1995). "The category of representations of the general linear groups over a finite field". Journal of Algebra. 176 (3): 908–946. doi:10.1006/jabr.1995.1278. MR 1351369.
• Street, Ross (1995). "Ideals, radicals, and structure of additive categories". ACS. 3 (2): 139–149. doi:10.1007/BF00877633. MR 1329188.
• Day, Brian; Street, Ross (1995). "Kan extensions along promonoidal functors". TAC. 1 (4): 72–78. MR 1333383.
• Freyd, Peter; Street, Ross (1995). "On the size of categories". TAC. 1 (9): 174–181. MR 1363007.
• Street, Ross (1995). "Low-dimensional topology and higher-order categories" (PDF). Proceedings of CT95 (Category Theory 1995). pp. 1–26.
• Street, Ross (1996). "Categorical Structures".In Hazewinkel, M. (ed.). Handbook of Algebra, Volume 1. Handbook of Algebra. 1. Elsevier Science. pp. 529–577. doi:10.1016/S1570-7954(96)80019-2. ISBN 978-0-444-82212-3. This article is available from the author here.
• Joyal, André; Street, Ross; Verity, Dominic (1996). "Traced monoidal categories". Math. Proc. Camb. Phil. Soc. 119 (3): 447–468. Bibcode:1996MPCPS.119..447J. doi:10.1017/S0305004100074338. MR 1357057.
• Day, Brian; Street, Ross (1997). "Monoidal bicategories and Hopf algebroids". Advances in Mathematics. 129 (1): 99–157. doi:10.1006/aima.1997.1649. MR 1458415.
• Street, Ross (1998). "Fusion operators and cocycloids in monoidal categories". ACS. 6 (2): 177–191. doi:10.1023/A:1008655911796. MR 1629381.
• Street, Ross (1998). "The quantum double and related constructions". JPAA. 132 (2): 195–206. doi:10.1016/S0022-4049(97)00111-4. MR 1640091.
• Street, Ross (1998). "The role of Michael Batanin's monoidal globular categories".In Getzler, E.; Kapranov, M. (eds.). Higher Category Theory : Workshop on Higher Category Theory and Physics, March 28-30, 1997, Northwestern University, Evanston, IL. Contemporary Math. 230. pp. 99–116. MR 1664994.
• Freyd, P.J.; O'Hearn, P.W.; Power, A.J.; Takeyama, M.; Street, R.; Tennent, R.D. (1999). "Bireflectivity". Theoretical Computer Science. 228 (1–2): 49–76. doi:10.1016/S0304-3975(98)00354-5. MR 1716746.
• Janelidze, George; Street, Ross (1999). "Galois theory in symmetric monoidal categories". Journal of Algebra. 220 (1): 174–187. doi:10.1006/jabr.1999.7905. MR 1713437.

2000

• Batanin, Michael; Street, Ross (2000). "The universal property of the multitude of trees". JPAA. 154 (1–3): 3–13. doi:10.1016/S0022-4049(99)00184-X. MR 1787588.
• Street, Ross (2000). "The petit topos of globular sets". JPAA. 154 (1–3): 299–315. doi:10.1016/S0022-4049(99)00183-8. MR 1787605.
• Kelly, Max; Labella, Anna; Schmitt, Vincent; Street, Ross (2002). "Categories enriched on two sides (Dedicated to Saunders Mac Lane on his 90th birthday)". JPAA. 168 (1): 53–98. doi:10.1016/S0022-4049(01)00048-2. MR 1879931.
• Davydov, Alexei; Street, Ross (2002). "Roots of unity as a Lie algebra" (PDF). Georgian Mathematical Journal. 9 (4): 683–690. MR 1971405.
• Street, Ross (2003). "Functorial calculus in monoidal bicategories". ACS. 11 (3): 219–227. doi:10.1023/A:1024247613677. MR 1990033.
• Day, Brian; McCrudden, Paddy; Street, Ross (2003). "Dualizations and Antipodes". ACS. 11 (3): 229–260. doi:10.1023/A:1024236601870. MR 1990034. Part of this paper was presented in: Street, Ross (September 24, 2002). "Formal representation theory". Toronto, Canada: Fields Institute. Invited talk at the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories. The URL for the title links to slides for, and an audio of, the talk.
• Day, Brian; Street, Ross (2003). "Abstract substitution in enriched categories". JPAA. 179 (1–2): 49–63. doi:10.1016/S0022-4049(02)00291-8. MR 1957814.
• Day, Brian J.; Street, Ross (2003). "Lax monoids, pseudo-operads, and convolution". Diagrammatic Morphisms and Applications. Contemporary Math. 318. pp. 75–96. ISBN 978-0-8218-2794-9. MR 1973511.
• Street, Ross (2003). "Weak omega-categories". Diagrammatic Morphisms and Applications. Contemporary Math. 318. pp. 207–213. ISBN 978-0-8218-2794-9. MR 1973518.
• Day, Brian J.; Street, Ross (2004). "Quantum categories, star autonomy, and quantum groupoids". Galois Theory, Hopf Algebras, and Semiabelian Categories. Fields Institute Communications. 43. pp. 187–226. arXiv:math.CT/0301209.
• Street, Ross (2004). "Categorical and combinatorial aspects of descent theory". ACS. 12 (5–6): 537–576. arXiv:math.CT/0303175. doi:10.1023/B:APCS.0000049317.24861.36. MR 2107402. See also: Street's 11 July 2003 lecture at ICIAM 2003.
• Street, Ross (2004). "The monoidal centre as a limit". TAC. 13 (13): 184–190. MR 2116332.
• Street, Ross (2004). "Frobenius monads and pseudomonoids". Journal of Mathematical Physics. 45 (10): 3930–3948. Bibcode:2004JMP....45.3930S. doi:10.1063/1.1788852. MR 2095680.
• Dubuc, Eduardo J.; Street, Ross (2006). "A construction of 2-filtered bicolimits of categories". CTGDC. 47 (2): 83–106. arXiv:math.CT/0605304. MR 2248225.
• Panchadcharam, Elango; Street, Ross (2006). "Pullback and finite coproduct preserving functors between categories of permutation representations". TAC. 16 (28): 771–784.
• Day, Brian; Street, Ross (2007). "Centres of monoidal categories of functors". Categories in Algebra, Geometry and Mathematical Physics. Contemporary Math. 431. pp. 187–202. ISBN 978-0-8218-3970-6.
• Day, Brian; Panchadcharam, Elango; Street, Ross (2007). "Lax braidings and the lax centre". Hopf Algebras and Generalizations. Contemporary Math. 441. pp. 1–17. ISBN 978-0-8218-3820-4.
• Panchadcharam, Elango; Street, Ross (2007). "Mackey functors on compact closed categories". Journal of Homotopy and Related Structures. 2 (2): 261–293. arXiv:0706.2922. Bibcode:2007arXiv0706.2922S.
• Street, Ross (2007). Quantum Groups : A Path to Current Algebra. Australian Mathematical Society Lecture Series. 19. Cambridge University Press. pp. 1–160. ISBN 9780521695244. MR 2294803.
• Carboni, A.; Kelly, G. M.; Walters, R. F. C.; Wood, R. J. (2008). "Cartesian bicategories II". TAC. 19 (6): 93–124. "The notion of cartesian bicategory, introduced by Carboni and Walters for locally ordered bicategories, is extended to general bicategories. It is shown that a cartesian bicategory is a symmetric monoidal bicategory."
• Walters, R. F. C.; Wood, R. J. (2008). "Frobenius objects in cartesian bicategories". TAC. 20 (3): 25–47.
• Pastro, Craig; Street, Ross (2008). "Doubles for monoidal categories". TAC. 21 (4): 61–75. arXiv:0711.1859. Bibcode:2007arXiv0711.1859P.
• Pastro, Craig; Street, Ross (2009). "Closed categories, star-autonomy, and monoidal comonads". Journal of Algebra. 321 (11): 3494–3521. arXiv:0712.0418. doi:10.1016/j.jalgebra.2008.05.004.
• Pastro, Craig; Street, Ross (2009). "Weak Hopf monoids in braided monoidal categories". Algebra and Number Theory. 3 (2): 149–207. arXiv:0801.4067. doi:10.2140/ant.2009.3.149. For a link to the complete issue containing this article, click here.
• Street, Ross (2009). "Weak distributive laws". TAC. 22 (12): 313–320.

2010

• Street, Ross (2010) [2004]. "An Australian Conspectus of Higher Categories".In Baez, John C.; May, J. Peter (eds.). Towards Higher Categories. The IMA Volumes in Mathematics and its Applications. 152. Springer-Verlag. pp. 237–264. doi:10.1007/978-1-4419-1524-5_6. ISBN 978-1-4419-1523-8. This paper is available from the author here.
• McCurdy, Micah; Street, Ross (2010). "What separable Fröbenius monoïdal functors preserve?". CTGDC. 51 (1): 29–50. arXiv:0904.3449. Bibcode:2009arXiv0904.3449B. MR 2650578. Zbl 1214.18008.
• Verity, Dominic; Street, Ross (2010). "The comprehensive factorization and torsors". TAC. 23 (3): 42–75.
• Chikhladze, Dimitri; Lack, Stephen; Street, Ross (2010). "Hopf monoidal comonads". TAC. 24 (19): 554–563. arXiv:1002.1122. Bibcode:2010arXiv1002.1122C.
• López Franco, Ignacio; Street, Ross; Wood, Richard (2011). "Duals Invert". ACS. 19 (1): 321–361. doi:10.1007/s10485-009-9210-7.
• Brown, Ronald; Street, Ross (2011). "Covering morphisms of crossed complexes and of cubical omega-groupoids are closed under tensor product". CTGDC. 52 (3): 188–208. arXiv:1009.5609. Bibcode:2010arXiv1009.5609B. MR 2866503. Zbl 1242.18004.
• Böhm, Gabriella; Lack, Stephen; Street, Ross (2011). "Weak bimonads and weak Hopf monads". Journal of Algebra. 328 (1): 1–30. arXiv:1002.4493. doi:10.1016/j.jalgebra.2010.07.032.
• Böhm, Gabriella; Lack, Stephen; Street, Ross (2011). "On the 2-Categories of Weak Distributive Laws". Communications in Algebra. 39 (12): 4567–4583. arXiv:1009.3454. doi:10.1080/00927872.2011.616436.
• Booker, Thomas; Street, Ross (2011). "Torsors, herds and flocks". Journal of Algebra. 330 (1): 346–374. arXiv:0912.4551. doi:10.1016/j.jalgebra.2010.12.009.
• Street, Ross (2012). "The core of adjoint functors". TAC. 27 (4): 47–64. arXiv:1112.0094. Bibcode:2011arXiv1112.0094S.
• Street, Ross (2012). "Monoidal categories in, and linking, geometry and algebra". Bulletin of the Belgian Mathematical Society - Simon Stevin. 19 (5): 769–820. arXiv:1201.2991. Bibcode:2012arXiv1201.2991S. Begins with an elementary introduction to the subject.
• Street, Ross (2012). "Parenthetic Remarks".In Müller-Hoissen, F.; Pallo, J.; Stasheff, J. (eds.). Associahedra, Tamari Lattices and Related Structures : Tamari Memorial Festschrift. Progress in Mathematics. 299. Basel: Birkhäuser. pp. 251–268. doi:10.1007/978-3-0348-0405-9_12. ISBN 978-3-0348-0404-2. See also "Parenthetic Remarks", a 1997 15-page preprint.
• Booker, Thomas; Street, Ross (2013). "Tannaka duality and convolution for duoidal categories". TAC. 28 (6): 166–205. arXiv:1111.5659. Bibcode:2011arXiv1111.5659B.
• Lack, Stephen; Street, Ross (2015). "Combinatorial categorical equivalences of Dold-Kan type". JPAA. 219 (10): 4343–4367. arXiv:1402.7151. doi:10.1016/j.jpaa.2019.07.002. The arXiv version contains several corrections to the published paper; the DOI link is to the 2019 Corrigendum to the original 2015 paper.
• Street, Ross (2015). "Kan extensions and cartesian monoidal categories". Seminarberichte der Mathematik. 87: 89–96. arXiv:1409.6405. Bibcode:2014arXiv1409.6405S.
• Street, Ross (2016). "Weighted tensor products of Joyal species, graphs, and charades". Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 12: 005. arXiv:1503.02783. Bibcode:2016SIGMA..12..005S. doi:10.3842/SIGMA.2016.005.
• Garner, Richard; Street, Ross (2016). "Coalgebras governing both weighted Hurwitz products and their pointwise transforms". Bulletin of the Belgian Mathematical Society - Simon Stevin. 23 (5): 643–666. arXiv:1510.05323. Bibcode:2015arXiv151005323G.
• Porst, Hans-E.; Street, Ross (2016). "Generalizations of the Sweedler Dual". ACS. 24 (5 : Special issue dedicated to the memory of Professor Horst Herrlich): 619–647. arXiv:1510.01797. doi:10.1007/s10485-016-9450-2.
• Street, Ross (2017). "Wreaths, mixed wreaths and twisted coactions". Tbilisi Mathematical Journal. 10 (3 : Special Issue in honor of Professors Peter J. Freyd and F.William Lawvere on the occasion of their 80th birthdays): 1–22. arXiv:1610.07281. doi:10.1515/tmj-2017-0100.
• Street, Ross (2017). "Categories in categories, and size matters". Higher Structures. 1 (1): 225–270. This paper is available from the author here.
• Janelidze, George; Street, Ross (2017). "Real sets". Tbilisi Mathematical Journal. 10 (3 : Special Issue in honor of Professors Peter J. Freyd and F.William Lawvere on the occasion of their 80th birthdays): 23–49. arXiv:1704.08787. doi:10.1515/tmj-2017-0101. "we define a category which provides an answer to the questions: what is a set with half an element? what is a set with π elements?" The arXiv version of 2018-01-16 points out that Examples 5.5 and 5.6 in the published paper are not in fact examples of series monoidal categories. This paper is summarized and discussed at The n-Category Café.
• Janelidze, George; Street, Ross (2018). "Infinitary addition, real numbers, and taut monads". ACS. 26 (5): 1047–1064. doi:10.1007/s10485-018-9524-4.
• Nikolić, Branko; Street, Ross (2018). "Extension creation under comonadic base change". arXiv:1809.02356 [math.CT].
• Nikolić, Branko; Street, Ross (2018). "Hopf rings for grading and differentials". arXiv:1806.09318 [math.CT].

Homological algebra

• Street, Ross H. (September 1968). Homotopy Classification of Filtered Complexes (PDF) (Thesis). University of Sydney. p. 137. : Street's Ph.D. thesis
• Street, Ross H. (September 1971). "Projective diagrams of interlocking sequences". Illinois Journal of Mathematics. 15 (3): 429–441. doi:10.1215/ijm/1256052612. MR 0279155. Zbl 0217.34801.
• Street, Ross (May 1973). "Homotopy classification of filtered complexes". J. Austral. Math. Soc. 15 (3): 298–318. doi:10.1017/S1446788700013227.
• Street, Ross (1984). "Homotopy classification by diagrams of interlocking sequences" (PDF). Math. Colloquium University of Cape Town. 13: 83–120. MR 0757459.

Monads

• Street, Ross (1972). "The formal theory of monads". JPAA. 2 (2): 149–168. doi:10.1016/0022-4049(72)90019-9. MR 0299653.
• Lack, Stephen; Street, Ross (2002). "The formal theory of monads II". JPAA. 175 (1–3): 243–265. doi:10.1016/S0022-4049(02)00137-8. MR 1935981.
• Böhm, Gabriella; Lack, Stephen; Street, Ross (2012). "Idempotent splittings, colimit completion, and weak aspects of the theory of monads". JPAA. 216 (2): 385–403. arXiv:1102.4931. doi:10.1016/j.jpaa.2011.07.003.
• Lack, Stephen; Street, Ross (2014). "On monads and warpings" (PDF). CTGDC. 55 (4): 244–266. arXiv:1408.4953. Bibcode:2014arXiv1408.4953L.

Relaxing the unit constraint

• Lack, Stephen; Street, Ross (2012). "Skew monoidales, skew warpings and quantum categories". TAC. 26 (15): 385–402. arXiv:1205.0074. Bibcode:2012arXiv1205.0074L.
• Street, Ross (2013). "Skew-closed categories". JPAA. 217 (6): 973–988. arXiv:1205.6522. doi:10.1016/j.jpaa.2012.09.020. "the author felt the time ripe to publish a reworking of Eilenberg and Kelly’s original paper on closed categories appropriate to the laxer context."
• Lack, Stephen; Street, Ross (2014). "A Skew-Duoidal Eckmann-Hilton Argument and Quantum Categories". ACS. 22 (5–6): 789–803. arXiv:1210.8192. doi:10.1007/s10485-013-9356-1.
• Lack, Stephen; Street, Ross (2014). "Triangulations, orientals, and skew monoidal categories". Advances in Mathematics. 258: 351–396. arXiv:1302.4488. doi:10.1016/j.aim.2014.03.003. "A concrete model of the free skew-monoidal category ${\displaystyle {\bf {Fsk}}}$ on a single generating object is obtained."
• Buckley, Mitchell; Garner, Richard; Lack, Stephen; Street, Ross (2015). "The Catalan simplicial set". Math. Proc. Camb. Phil. Soc. 158 (2): 211–222. arXiv:1309.6120. Bibcode:2015MPCPS.158..211B. doi:10.1017/S0305004114000498. Earlier version: Buckley, Mitchell; Garner, Richard; Lack, Stephen; Street, Ross (2013). "Skew-monoidal categories and the Catalan simplicial set": 1–15. arXiv:1307.0265. Bibcode:2013arXiv1307.0265B.
• Lack, Stephen; Street, Ross (2015). "Skew-monoidal reflection and lifting theorems". TAC. 30 (28): 985–1000. arXiv:1410.6972. Bibcode:2014arXiv1410.6972L.

An excerpt from Street's web page.

• Two unpublished manuscripts on topos theory: Street, Ross (January 1974). "Lectures on topos theory" (PDF). Monash University. pp. 1–27. (Handwritten manuscript); Street, Ross (April 1978). "A survey of topos theory" (PDF). pp. 1–61. (Typed manuscript).
• Street, Ross (February 1985). "Cohomology of groups" (PDF). pp. 1–17. Handwritten manuscript. See also: Street, Ross (October 2001). "The 3-cocycle condition" (PDF). pp. 1–3.
• Eilenberg, Samuel; Street, Ross (c. 1986). "Rewrite systems, algebraic structures, and higher-order categories" (PDF). pp. 1–62. Handwritten undated manuscript (31 PDF pages).
• Street, Ross (February 1988). "Gray's tensor product of 2-categories" (PDF). pp. 1–22. Handwritten manuscript. Defines the Gray tensor product on 2-Cat as the left Kan extension of a geometrically natural tensor product defined on a full dense subcategory ("Cu") of 2-Cat.
• Joyal, André; Street, Ross (1995). "The geometry of tensor calculus II" (PDF). pp. 1–18. "[T]his paper gives the precise modification of the string diagrams in monoidal (also called 'tensor') categories required to accommodate the existence

of dual objects."

• Street, Ross (February 1998). "Monoidal categories for the combinatorics of group representations" (PDF). pp. 1–7. Basic category theory applied to combinatorial finite set theory, linear algebra, and group representations.
• Street, Ross (May 2002). "Trees, permutations and the tangent function" (PDF). Reflections. 27 (2): 19–23. arXiv:math.HO/0303267.beamer version
• Street, Ross (September 2004). "Frobenius algebras and monoidal categories" (PDF). pp. 1–19. Slides from a talk at the annual meeting of the Australian Mathematical Society.
• Street, Ross (2014-09-24). "Pointwise extensions and sketches in bicategories". arXiv:1409.6427 [math.CT].