1995/03/31 by John C. Baez, James Dolan · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #hep-th #math.CT #math.QA #q-alg
paper · pdf · doi:10.1063/1.531236
published as J.Math.Phys. 36 (1995) 6073-6105 · 36 pages, LaTeX; this version includes all 36 figures
openalex publication_date 1995/11/01 · arxiv created 2004/03/06 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 topological quantum field theories (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.