The notion of Morita equivalence (in its various incarnations: algebras, $C^*$-algebras, von Neumann algebras, Poisson manifolds, Lie groupoids, orbifolds, algebraic stacks) is illuminated by higher category theory. Ok... not so high. See e.g. this paper for a short survey.
The notion of Morita equivalence (in its various incarnations: algebras, $C^*$-algebras, von Neumann algebras, Poisson manifolds, orbifolds) is illuminated by higher category theory. Ok... not so high. See e.g. this paper for a short survey.