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

Abstract

We prove cocontinuity of the \max -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 \mathrm{II}_{1} -factor, enhancing a realization theorem due to C. Jones and D. Penneys.