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Explore the concept of Möbius cohomology in this 51-minute lecture from the Applied Algebraic Topology Network. Learn how Möbius cohomology is defined as the derived functors of an enriched hom-functor between P-modules, following the recent introduction of Möbius homology by Patel and Skraba as a categorification of Möbius inversion. Discover how the Euler characteristic of Möbius cohomology recovers the Möbius inversion of the dimension function of the module. The lecture also covers Galois connections, demonstrating how Rota's Galois Connection Theorem emerges naturally as an enriched adjunction induced by a Galois connection.
