Homotopy quantum field theories and tortile structures

الأصل · EN

We study a variation of 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 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, under certain conditions, an ₓ-structure gives rise to a lax tortile π-category when the background space is an Eilenberg-Maclane space X=K(π,1), and to a tortile category with lax π₂X-action when the background space is simply-connected.