dorsal/arxiv
View SchemaHigher-dimensional Algebra and Topological Quantum Field Theory
| Authors | John C. Baez, James Dolan |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9503002 |
| URL | https://arxiv.org/abs/q-alg/9503002 |
| DOI | 10.1063/1.531236 |
| Journal | J.Math.Phys. 36 (1995) 6073-6105 |
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.
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"abstract": "The study of topological quantum field theories increasingly relies upon\nconcepts from higher-dimensional algebra such as n-categories and n-vector\nspaces. We review progress towards a definition of n-category suited for this\npurpose, and outline a program in which n-dimensional TQFTs are to be described\nas n-category representations. First we describe a \"suspension\" operation on\nn-categories, and hypothesize that the k-fold suspension of a weak n-category\nstabilizes for k \u003e= n+2. We give evidence for this hypothesis and describe its\nrelation to stable homotopy theory. We then propose a description of\nn-dimensional unitary extended TQFTs as weak n-functors from the \"free stable\nweak n-category with duals on one object\" to the n-category of \"n-Hilbert\nspaces\". We conclude by describing n-categorical generalizations of deformation\nquantization and the quantum double construction.",
"arxiv_id": "q-alg/9503002",
"authors": [
"John C. Baez",
"James Dolan"
],
"categories": [
"q-alg",
"hep-th",
"math.CT",
"math.QA"
],
"doi": "10.1063/1.531236",
"journal_ref": "J.Math.Phys. 36 (1995) 6073-6105",
"title": "Higher-dimensional Algebra and Topological Quantum Field Theory",
"url": "https://arxiv.org/abs/q-alg/9503002"
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