case in [@bunketurnerwillerton](See also [@BunkWaldorf] for the open-closed case). Our results can be seen as a higher categorical, but purely topological version of this approach.

This paper is organized as follows: In Section \[secexthqft\] we recall the notion of an extended homotopy quantum field theory as introduced in [@extofk] generalizing [@turaevhqft]. Then, given an $n$-cocycle $\theta \in Z^n(T;{\operatorname{U}}(1))$ on a space $T$, we construct in Section \[secconstruchqft\] an extended homotopy quantum field theory $T_\theta$ with target space $T$ (Theorem \[mainthm\]) that can be understood as an extended version of the primitive homotopy quantum field theory. In physical terms it should be understood as the parallel transport operator for the flat gerbe $\theta$ from which the Wess-Zumino terms can be obtained.

In Section \[sectransgression\] we explore the relation between extended primitive homotopy quantum field theories and transgression. More precisely, we prove that for a cocycle $\theta \in Z^n(BG;{\operatorname{U}}(1))$ the associated extended field theory gives rise to a 2-line bundle over the groupoid of $G$-bundles over any closed oriented $n-2$-dimensional manifold, which is entirely determined by a transgression of $\theta$ (Theorem \[Theorem: Transgression\]).

When combined with the orbifold construction from [@extofk], our extended primitive theories allow for a very elegant description of 