  In this note we review how both derived categories and stacks enter physics.
The physical realization of each has many formal similarities. For example, in
both cases, equivalences are realized via renormalization group flow: in the
case of derived categories, (boundary) renormalization group flow realizes the
mathematical procedure of localization on quasi-isomorphisms, and in the case
of stacks, worldsheet renormalization group flow realizes
presentation-independence. For both, we outline current technical issues and
applications.
