A persistence Spanier-Whitehead category of filtered CW complexes is defined, proven to be a triangulated persistence category, and its K-group is shown to be isomorphic to the Novikov polynomial ring via the weighted Euler characteristic.
Borceux, Handbook of Categorical Algebra: Basic category theory
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Filtered Topology and Persistence in Stable Homotopy
A persistence Spanier-Whitehead category of filtered CW complexes is defined, proven to be a triangulated persistence category, and its K-group is shown to be isomorphic to the Novikov polynomial ring via the weighted Euler characteristic.