An Australian conspectus of higher categories - Macquarie University

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[Seg] G. Segal, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math. 34 (1968) 105-112. [Sh] M.C. Shum, Tortile Tensor Categories, PhD Thesis, Macquarie University (November 1989); J. Pure Appl. Algebra 93 (1994) 57-110. [St1] R. Street, Homotopy Classification of Filtered Complexes, PhD Thesis, University of Sydney, August 1968. [St2] R. Street, The formal theory of monads, J. Pure Appl. Algebra 2 (1972) 149-168; MR45#8701. [St3] R. Street, Two constructions on lax functors, Cahiers topologie et géométrie différentielle 13 (1972) 217-264. [St4] R. Street, Homotopy classification of filtered complexes, J. Australian Math. Soc. 15 (1973) 298-318. [St5] R. Street, Fibrations and Yoneda's lemma in a 2-category, in: "Category Seminar (Proc. Sem., Sydney, 1972/1973)" Lecture Notes in Math. 420 (Springer, Berlin, 1974) 104-133. [St6] R. Street, Elementary cosmoi I, in: "Category Seminar (Proc. Sem., Sydney, 1972/1973)" Lecture Notes in Math. 420 (Springer, Berlin, 1974) 134-180. [St7] R. Street, Limits indexed by category-valued 2-functors, J. Pure Appl. Algebra 8 (1976) 149-181. [St8] R. Street, Cosmoi of internal categories, Transactions American Math. Soc. 258 (1980) 271-318. [St9] R. Street, Fibrations in bicategories, Cahiers topologie et géométrie différentielle 21 (1980) 111-160. [St10] R. Street, Conspectus of variable categories, J. Pure Appl. Algebra 21 (1981) 307-338. [St11] R. Street, (see [St31]) Cauchy characterization of enriched categories, Rendiconti del Seminario Matematico e Fisico di Milano 51 (1981) 217-233. [St12] R. Street, Two dimensional sheaf theory, J. Pure Appl. Algebra 23 (1982) 251-270; MR83d:18014. [St13] R. Street, Characterization of bicategories of stacks, Lecture Notes in Math. 962 (1982) 282-291. [St14] R. Street, Enriched categories and cohomology, Quaestiones Math. 6 (1983) 265-283. [St15] R. Street, Absolute colimits in enriched categories, Cahiers topologie et géométrie différentielle 24 (1983) 377- 379. [St16] R. Street, Homotopy classification by diagrams of interlocking sequences, Math. Colloquium University of Cape Town 13 (1984) 83-120. [St17] R. Street, The algebra of oriented simplexes, J. Pure Appl. Algebra 49 (1987) 283-335. [St18] R. Street, Correction to "Fibrations in bicategories", Cahiers topologie et géométrie différentielle catégoriques 28 (1987) 53-56. [St19] R. Street, Fillers for nerves, Lecture Notes in Math. 1348 (1988) 337-341. [St20] R. Street, Parity complexes, Cahiers topologie et géométrie différentielle catégoriques 32 (1991) 315-343. [St21] R. Street, Categorical structures, Handbook of Algebra Volume 1 (editor M. Hazewinkel; Elsevier Science, Amsterdam 1996; ISBN 0 444 82212 7) 529-577. [St22] R. Street, Higher categories, strings, cubes and simplex equations, Applied Categorical 28
Structures 3 (1995) 29- 77 & 303. [St23] R. Street, Parity complexes: corrigenda, Cahiers topologie et géométrie différentielle catégoriques 35 (1994) 359-361. [St24] R. Street, Low-dimensional topology and higher-order categories, Proceedings of CT95, Halifax, July 9-15 1995; . [St25] R. Street, The role of Michael Batanin's monoidal globular categories, in: "Higher Category Theory" (editors E. Getzler and M. Kapranov) Contemporary Mathematics 230 (A.M.S. 1998) 99-116. [St26] R. Street, The petit topos of globular sets, J. Pure Appl. Algebra 154 (2000) 299-315. [St27] R. Street, Functorial calculus in monoidal bicategories, Applied Categorical Structures 11 (2003) 219-227. [St28] R. Street, Weak omega-categories, in: "Diagrammatic Morphisms and Applications", Contemporary Mathematics 318 (AMS; ISBN 0-8218-2794-4; April 2003) 207-213. [St29] R. Street, Categorical and combinatorial aspects of descent theory, Applied Categorical Structures 12 (2004) 537-576. [St30] R. Street, Frobenius monads and pseudomonoids, J. Math. Phys. 45(10) (October 2004) 3930-3948. [St31] R. Street, (see [St11]) Cauchy characterization of enriched categories, Reprints in Theory and Applications of Categories 4 (2004) 1-16. [StW] R. Street and R.F.C. Walters, Yoneda structures on 2-categories, J. Algebra 50 (1978) 350-379. [Ta] Z. Tamsamani, Sur des notions de n-categorie et n-groupoide non-stricte via des ensembles multisimpliciaux, K-Theory16 (1999) 51-99. [Tr] T. Trimble, The definition of tetracategory (handwritten diagrams; August 1995). [Tu] V.G. Turaev, The Yang-Baxter equation and invariants of links, Invent. Math. 92 (1988) 527-553. [V] D. Verity, Characterization of cubical and simplicial nerves, math.CT/0410412 . [Wa] R.F.C. Walters, Sheaves on sites as Cauchy-complete categories, J. Pure Appl. Algebra 24 (1982) 95-102. [Wo] H. Wolff, V -cat and V -graph, J. Pure Appl. Algebra 4 (1974) 123-135. [Z] V. Zöberlein, Doctrines on 2-categories, Math. Z. 148 (1976) 267-279 (originally Doktrinen auf 2- Kategorien, Manuscript, Math. Inst. Univ. Zürich, 1973). Centre of Australian Category Theory Macquarie University New South Wales 2109 AUSTRALIA email: street@math.mq.edu.au homepage: 29
Page 1 and 2: An Australian conspectus of higher
Page 3 and 4: Cat co ). In stark contrast with to
Page 5 and 6: pointed out the colimit- and limit-
Page 7 and 8: construction which in Cat forms the
Page 9 and 10: object U of C , the category FU is
Page 11 and 12: (strict) n-categories because he th
Page 13 and 14: "from the top down". The paper [St1
Page 15 and 16: turned braids into links. In the mi
Page 17 and 18: where we write S for the formal sum
Page 19 and 20: of it using Yang-Baxter operators.
Page 21 and 22: "Oh Ross, have you . . . ?", that s
Page 23 and 24: [Car] S.M. Carmody, Cobordism Categ
Page 25 and 26: [Gr14] J.W. Gray, The representatio
Page 27: [Ko1] A. Kock, Monads for which str

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