## Abstract

We study a version of a modular functor for Turaev's homotopy quantum field theories using 2-categories of surfaces. We define the homotopy surface 2-category of a space X and define an S_{X}-structure to be a monoidal 2-functor from this to the 2-category of idempotent-complete additive k-linear categories. We initiate the study of the algebraic structure arising from these functors. In particular we show that a unitary S_{X}-structure gives rise to a lax tortile p-category when the background space is an Eilenberg-Maclane space X=K(p,1), and to a tortile category with lax p_{2}X-action when the background space is simply connected. © 2003. Published by Elsevier B.V.

Original language | English |
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Pages (from-to) | 43-71 |

Number of pages | 29 |

Journal | Journal of Pure and Applied Algebra |

Volume | 185 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 1 Dec 2003 |