Ross Street is a major member of the Australian school of higher category theory, a student and collaborator of the late Gregory Maxwell Kelly.
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.
On lax functors:
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:
On Frobenius monads:
An attempt to fomulate descent theory using strict omega-categories:
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):
On coherence theorems for tricategories:
On bireflective subcategories with ambidextrous adjoints:
On comprehensive factorization systems and torsors:
On the history of Australian higher category theory (such as the role of Roberts (1979)):
Last revised on May 10, 2023 at 05:15:31. See the history of this page for a list of all contributions to it.