  We give another definition of two-dimensional extended homotopy field
theories (E-HFTs) with aspherical targets and classify them. When the target of
E-HFT is chosen to be a $K(G,1)$-space, we classify E-HFTs taking values in the
symmetric monoidal bicategory of algebras, bimodules, and bimodule maps by
certain Frobenius $G$-algebras called quasi-biangular $G$-algebras. As an
application, for any discrete group $G$, we verify a special case of the $(G
\times SO(2))$-structured cobordism hypothesis due to Lurie.
