Abstract: Möbius homology was recently introduced by Patel and Skraba and provides a categorification of Möbius inversion. In this talk, we’ll define Möbius homology and cohomology as the derived functors of an enriched hom-functor between P-modules. We’ll then show that the Euler characteristic of Möbius cohomology recovers the Möbius inversion of the dimension function of the module. Finally, we’ll discuss Galois connections and show that Rota’s Galois Connection Theorem appears naturally in this setting as an enriched adjunction induced by a Galois connection.