Operads, modules and topological field theories
Abstract
In this paper, we describe a general theory of modules over an algebra over an operad. We also study functors between categories of modules. Specializing to the operad E_d of little ddimensional disks, we show that each (d1)manifold gives rise to a theory of modules over E_dalgebras and each bordism gives rise to a functor from the category defined by its incoming boundary to the category defined by its outgoing boundary. We describe how to assemble these categories into a map from a certain operad to the operad of (infinity)categories.
 Publication:

arXiv eprints
 Pub Date:
 May 2014
 arXiv:
 arXiv:1405.5409
 Bibcode:
 2014arXiv1405.5409H
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Quantum Algebra
 EPrint:
 44 pages