nLab Ross Street

Ross Street is a major member of the Australian school of higher category theory, a student and collaborator of the late Gregory Maxwell Kelly.

• homepage

His most important works include works in sheaf-, fibred category-, and descent-theory, including the introduction of orientals, a definition of weak higher category, braided categories and quantum groups, Tannaka reconstruction, categorical algebra (e.g. formal theory of monads), bicategories, coherence theorems for tricategories, etc.

Selected writings

• list of publications

On lax functors:

• R. Street, Two constructions on lax functors, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume 13 (1972) no. 3 , p. 217-264 numdam

On the 2-category theory of monads and their Eilenberg-Moore categories:

• Ross Street, The formal theory of monads, Journal of Pure and Applied Algebra 2 2 (1972) 149-168 [doi:10.1016/0022-4049(72)90019-9]

• Stephen Lack, Ross Street, The formal theory of monads II, Journal of Pure and Applied Algebra

  175 1–3 (2002) 243-265 [doi:10.1016/S0022-4049(02)00137-8]

Introducing the notion of orientals:

• Ross Street, The algebra of oriented simplexes, J. Pure Appl. Algebra 49 (1987) 283-335; [pdf, doi:10.1016/0022-4049(87)90137-X, MR89a:18019]

On Frobenius monads:

• Ross Street, Frobenius monads and pseudomonoids, J. Math. Phys. 45 3930 (2004) [doi:10.1063/1.1788852]

An attempt to fomulate descent theory using strict omega-categories:

• Ross Street, Categorical and combinatorial aspects of descent theory, Applied Categorical Structures 12, 537–576 (2004) doi

Further:

• A. Joyal, R. Street, Pullbacks equivalent to pseudopullbacks, Cahiers topologie et géométrie différentielle catégoriques 34 (1993) 153-156; numdam MR94a:18004.

• A. Joyal, R. Street, An introduction to Tannaka duality and quantum groups, Category theory (Como, 1990), 413–492, Lecture Notes in Math. 1488, Springer 1991 (pdf).

• A. Joyal, R. Street, The geometry of tensor calculus I, Adv. Math. 88(1991), no. 1, 55–112, doi; Tortile Yang-Baxter operators in tensor categories, J. Pure Appl. Algebra 71 (1991), no. 1, 43–51, doi; Braided tensor categories, Adv. Math. 102 (1993), no. 1, 20–78, doi.

• A. Joyal, R. Street, D. Verity, Traced monoidal categories. Math. Proc. Cambridge Philos. Soc. 119 (1996), no. 3, 447–468.

• R.H. Street, Fibrations in bicategories, Cahiers de topologie et géométrie différentielle XXI (1980) 111–160

• R.H. Street, Two dimensional sheaf theory, J. Pure and Appl. Algebra 24 (1982) MR617138

• R. Street, Characterization of bicategories of stacks, In: Kamps, K.H., Pumplün, D., Tholen, W. (eds) Category Theory. Lect. Notes Math. 962, Springer 1982 doi

On monoidal 2-categories, braided monoidal 2-categories, sylleptic monoidal 2-categories and symmetric monoidal 2-categories (and pseudomonoids):

• Brian Day, Ross Street, Monoidal bicategories and Hopf algebroids, Adv. Math. 129:1 (1997) 99-157 (doi:10.1006/aima.1997.1649)

On coherence theorems for tricategories:

• Robert Gordon, A. John Power, Ross Street, Coherence for tricategories, Mem. Amer. Math Soc. 117 (1995) no 558 (ISBN:978-1-4704-0137-5)

On bireflective subcategories with ambidextrous adjoints:

• Peter Freyd, Peter O’Hearn, A. John Power, M. Takeyama, Ross Street, Robert D. Tennent, Bireflectivity, Theoretical Computer Science 228 1–2 (1999) 49-76 [doi:10.1016/S0304-3975(98)00354-5]

On comprehensive factorization systems and torsors:

• Ross Street, Dominic Verity, The comprehensive factorization and torsors, TAC 23 (2010) 42-75 [tac:23-03]

On the history of Australian higher category theory (such as the role of Roberts (1979)):

• Ross Street, An Australian conspectus of higher category theory, talk at Institute for Mathematics and its Applications Summer Program: $n$-Categories: Foundations and Applications at the University of Minnesota (Minneapolis, 7–18 June 2004), in: Towards Higher Categories, The IMA Volumes in Mathematics and its Applications 152, Springer (2010) 237-264 [pdf, pdf, doi:10.1007/978-1-4419-1524-5]

On monoidal categories:

• Ross Street, Monoidal categories in, and linking, geometry and algebra, Bull. Belg. Math. Soc. Simon Stevin 19 5 (2012) 769-820 [arXiv:1201.2991, doi:10.36045/bbms/1354031551]

category: people