C${}^{\ast }$-algebraic factorization homology and realization of cyclic representations

Abstract

We prove cocontinuity of the $\max$-tensor product of C${}^{\ast }$-categories and develop a framework to perform factorization homology in a C${}^{\ast }$-setting. In such context, we specialize some results of D. Ben-Zvi, A. Brochier, and D. Jordan. As a consequence of our constructions, we realize quantum Hamiltonian reduction in terms of bimodules over a factor $N$. We also provide a GNS-type reconstruction theorem for C${}^{\ast }$-algebra objects in categories of bimodules over a ${\mathrm{II}}_1$-factor, enhancing a realization theorem due to C. Jones and D. Penneys.