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      Yoneda Structures from 2-toposes

      Applied Categorical Structures
      Springer Nature

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          Review of the elements of 2-categories

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            Higher-dimensional Algebra and Topological Quantum Field Theory

            The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and outline a program in which n-dimensional TQFTs are to be described as n-category representations. First we describe a "suspension" operation on n-categories, and hypothesize that the k-fold suspension of a weak n-category stabilizes for k >= n+2. We give evidence for this hypothesis and describe its relation to stable homotopy theory. We then propose a description of n-dimensional unitary extended TQFTs as weak n-functors from the "free stable weak n-category with duals on one object" to the n-category of "n-Hilbert spaces". We conclude by describing n-categorical generalizations of deformation quantization and the quantum double construction.
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              Limits indexed by category-valued 2-functors

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                Author and article information

                Journal
                Applied Categorical Structures
                Appl Categor Struct
                Springer Nature
                0927-2852
                1572-9095
                July 6 2007
                May 3 2007
                : 15
                : 3
                : 259-323
                Article
                10.1007/s10485-007-9079-2
                c1e9fa14-55ca-46f4-81a0-90ed2fe7c68e
                © 2007
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