nLab Ross Street

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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.

1. 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 sketches in the generality of internalization into 2-categories:

On topos theory:

Introducing the notion of braided monoidal categories:

On flexible limits:

Introducing the notion of traced monoidal categories:

On the Gray tensor product for 2-categories:

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

Introducing the notion of orientals:

On basic notions of 2-category theory:

On Frobenius monads:

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

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

Introducing skew-closed 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;

  • 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:

2. Collected writings

category: people

Last revised on September 1, 2024 at 08:09:04. See the history of this page for a list of all contributions to it.

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