The cobordism categories with defects

The cobordism hypothesis says, in its basic form, that a TQFT (on plain manifolds) are determined from its value on a point. One can consider more interesting TQFTs by allowing defects (singularities along a stratification) on manifolds. In this talk, I will describe a formal construction of such cobordism categories from the plain ones and how the cobordism hypothesis with defects follows from the plain ones as a formal consequence of (pre)stability of symmetric monoidal (infinity, n)-categories.