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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. That's an example of a notion that was first formulated without reference to higher categories, and later explained using that language. |
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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. That's an example of a notion that was first formulated without reference to higher categories, and later explained using that language. |
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