  We prove that a finite braided tensor category A is invertible in the Morita
4-category BrTens of braided tensor categories if, and only if, it is
non-degenerate. This includes the case of semisimple modular tensor categories,
but also non-semisimple examples such as categories of representations of the
small quantum group at good roots of unity. Via the cobordism hypothesis, we
obtain new invertible 4-dimensional framed topological field theories, which we
regard as a non-semisimple framed version of the Crane-Yetter-Kauffman
invariants, after Freed--Teleman and Walker's construction in the semisimple
case. More generally, we characterize invertibility for E_1- and E_2-algebras
in an arbitrary symmetric monoidal oo-category, and we conjecture a similar
characterization of invertible E_n-algebras for any n. Finally, we propose the
Picard group of BrTens as a generalization of the Witt group of non-degenerate
braided fusion categories, and pose a number of open questions about it.
