  This paper studies the basic K-theoretic properties of a triangulated
persistence category (TPC). This notion was introduced in our earlier papers on
triangulation, persistence, and Fukaya categories (arXiv:2304.01785 and
arXiv:2104.12258) and it is a type of category that can be viewed as a
refinement of a triangulated category in the sense that the morphisms sets of a
TPC are persistence modules. We calculate the K-groups in some basic examples
and discuss an application to Fukaya categories and to the topology of exact
Lagrangian submanifolds.
