C^*-algebraic factorization homology and realization of cyclic representations

We prove cocontinuity of the -tensor product of C ^* -categories and develop a framework to perform factorization homology in a C ^* -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 ^* -algebra objects in categories of bimodules over a II₁ -factor, enhancing a realization theorem due to C. Jones and D. Penneys.