Open modular functors from non-finite tensor categories

Abstract: We show that a compact rigid balanced braided monoidal category with enough compact projective objects gives rise to a system of mapping class group representations compatible with the gluing along marked intervals. A motivation to consider non-finite tensor categories is the theory of vertex operator algebras where such categories arise as categories of modules. The mapping class group representations presented in this article admit a factorization homology description. In other words, they are of three-dimensional origin and hence obey a holographic principle. A compact projective symmetric Frobenius algebra endows the representations with a pointing that is mapping class group invariant and compatible with the gluing along intervals. This shows that, at least to some extent, many of the tools for the construction and study of spaces of conformal blocks and correlators remain available in a non-finite, but rigid setting.