## Higher-Dimensional Algebra and Topological Quantum Field Theory (1995)

Venue: | Jour. Math. Phys |

Citations: | 139 - 14 self |

### BibTeX

@ARTICLE{Baez95higher-dimensionalalgebra,

author = {John C. Baez and James Dolan},

title = {Higher-Dimensional Algebra and Topological Quantum Field Theory},

journal = {Jour. Math. Phys},

year = {1995},

volume = {36},

pages = {6073--6105}

}

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### Abstract

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. Introduction One important lesson we have learned from topological quantum field theory is that describ...