Poincaré Duality for Generalized Persistence Diagrams of (Co)filtrations

We dualize previous work on generalized persistence diagrams for filtrationsto cofiltrations. When the underlying space is a manifold, we express thisduality as a Poincaré duality between their generalized persistence diagrams.A heavy emphasis is placed on the recent discovery of functoriality of thegeneralized persistence diagram and its connection to Rota's Galois ConnectionTheorem.