order to formulate this idea more precisely, we need to introduce a bit of terminology.

Let $M$ be a manifold of dimension $m \leq n$. An [*$n$-framing*]{} of $M$ is a trivialization of the vector bundle $T_{M} \oplus \underline{ {{\mathbb R}}^{n-m} }$, where $\underline{ {{\mathbb R}}^{n-m} }$ denotes the trivial bundle (on $M$) of rank $n-m$. We let ${\mathbf{Bord}}_{n}^{\operatorname{fr}}$ denote the bordism $n$-category whose $k$-morphisms are given by $n$-framed $k$-manifolds for $k \leq n$.

\[bd\] Let ${\mathcal{C}}$ be a symmetric monoidal $n$-category. Then the construction $$F \mapsto F(\ast)$$ induces an injection from the collection of isomorphism classes of symmetric monoidal functors $F: {\mathbf{Bord}}_{n}^{\operatorname{fr}} \rightarrow {\mathcal{C}}$ to the collection of isomorphism classes of objects of ${\mathcal{C}}$.

A version of Theorem \[bd\] was originally conjectured by Baez and Dolan in [@BD]. We refer the reader to [@L] for a more extensive discussion and a sketch of the proof.

Let ${\mathcal{C}}$ be a symmetric monoidal $n$-category. We will say that an object $C \in {\mathcal{C}}$ is [*fully dualizable*]{} if there exists an extended TQFT $F: {\mathbf{Bord}}_{n}^{\operatorname{fr}} \rightarrow {\mathcal{C}}$ and an isomorphism $C \simeq F(\ast)$. Theorem \[bd\] asserts that if $C$ is a fully dualizable object of ${\mathcal{C}}$, then the field theory $F$ is 