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.

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

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:

On enriched category theory and cosmoi:

On topos theory:

Introducing the notion of traced monoidal categories:

Introducing the notion of orientals:

On basic notions of 2-category theory:

On Frobenius monads:

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


  • 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.

  • 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)):

  • Ross Street, An Australian conspectus of higher category theory, talk at Institute for Mathematics and its Applications Summer Program: nn-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 lax braided monoidal categories with possibly non-invertible braiding:

On monoidal categories:

Collected writings


  • Ross Street, Complete objects relative to a theory, June 1976 (pdf)

  • Ross Street, Gray’s tensor product of 2-categories, February 1982, (pdf)

category: people

Last revised on November 28, 2023 at 15:11:27. See the history of this page for a list of all contributions to it.