Operads, modules and topological field theories
arXiv:1405.5409
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 d-dimensional disks, we show that each (d-1)-manifold gives rise to a theory of modules over E_d-algebras 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.
arXiv comment44 pages
References in corpus (11)
- Algebras and modules in monoidal model categories
- Constructing symmetric monoidal bicategories
- On the Multiplicative Structure of Topological Hochschild Homology
- From manifolds to invariants of E_n-algebras
- Operations on derived moduli spaces of branes
- Homotopical resolutions associated to deformable adjunctions
- Structured singular manifolds and factorization homology
- Factorization homology and calculus à la Kontsevich Soibelman
- Partial model categories and their simplicial nerves
- Derived Higher Hochschild Homology, Topological Chiral Homology and Factorization algebras
- Moduli spaces of algebras over non-symmetric operads