Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-05-13
7th Conference on Category Theory and Computer Science, eds. E. Moggi and G. Rosolini, Lecture Notes in Computer Science vol.
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
34 pages LaTeX, 30 encapsulated Postscript figures, 2 style files
Scientific paper
An n-category is some sort of algebraic structure consisting of objects, morphisms between objects, 2-morphisms between morphisms, and so on up to n-morphisms, together with various ways of composing them. We survey various concepts of n-category, with an emphasis on `weak' n-categories, in which all rules governing the composition of j-morphisms hold only up to equivalence. (An n-morphism is an equivalence if it is invertible, while a j-morphism for j < n is an equivalence if it is invertible up to a (j+1)-morphism that is an equivalence.) We discuss applications of weak n-categories to various subjects including homotopy theory and topological quantum field theory, and review the definition of weak n-categories recently proposed by Dolan and the author.
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