  The inclusion of the unit in a braided tensor category $\mathcal{V}$ induces
a 1-morphism in the Morita 4-category of braided tensor categories $BrTens$. We
give criteria for the dualizability of this morphism.\\ When $\mathcal{V}$ is a
semisimple (resp. non-semisimple) modular category, we show that the unit
inclusion induces under the Cobordism Hypothesis a (resp. non-compact) relative
3-dimensional topological quantum field theory. Following Jordan--Safronov, we
conjecture that these relative field theories together with their bulk theories
recover Witten--Reshetikhin--Turaev (resp. De
Renzi--Gainutdinov--Geer--Patureau-Mirand--Runkel) theories, in a fully
extended setting. In particular, we argue that these theories can be obtained
by the Cobordism Hypothesis.
