Hochschild Homology of Functors
The simplicial circle S1 is a simplicial object in the category Fin* of finite pointed sets, i.e. a functor Δo → Fin*. Thus, if F is a functor F: Fin → k-mod, we get a simplicial module by composing F with S1
The homology of this simplicial module is the Hochschild homology of the functor F. The above definition of Hochschild homology of commutative algebras is the special case where F is the Loday functor.
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