The above construction of the Hochschild complex can be adapted to more general situations, namely by replacing the category of (complexes of) formula_29-modules by an ∞-category (equipped with a tensor product) formula_114, and formula_30 by an associative algebra in this category. Applying this to the category formula_116 of spectra, and formula_30 being the Eilenberg–MacLane spectrum associated to an ordinary ring formula_118 yields topological Hochschild homology, denoted formula_119. The (non-topological) Hochschild homology introduced above can be reinterpreted along these lines, by taking for "formula_120" the derived category of formula_121-modules (as an ∞-category).