Baez–Dolan–Lurie cobordism hypothesis for framed manifolds

Let $\mathscr{C}$ be a symmetric monoidal infinity $n$-category. A fully dualizable object of $\mathscr{C}$ is an object satisfying the dualizability conditions at every categorical level, and let $\mathscr{C}^{\textnormal{fd}}$ denote the space of such objects. Baez–Dolan–Lurie conjecture. The space of 0-1-$\cdots$-$n$ theories of framed manifolds with values in $\mathscr{C}$ is homotopy equivalent to $\mathscr{C}^{\textnormal{fd}}$. This is the higher-dimensional generalization of the cobordism hypothesis and would classify framed fully extended topological field theories by fully dualizable objects; the source describes Lurie as having a detailed plan of proof, but does not establish the conjecture in full generality.