We introduce and study algebraic structures underlying –dimensional Homotopy Quantum Field Theories (HQFTs) with arbitrary target spaces. These algebraic structures are formalized in the notion of a twisted Frobenius algebra. Our work generalizes results of Brightwell, Turner and the second author on –dimensional HQFTs with simply connected or aspherical targets.
Mihai D Staic. Vladimir Turaev. "Remarks on $2$–dimensional HQFTs." Algebr. Geom. Topol. 10 (3) 1367 - 1393, 2010. https://doi.org/10.2140/agt.2010.10.1367