A lot of well-known functors such as group homology, cyclic homology of algebras can be described as limits of certain simply defined functors over categories of presentations. In this paper, we develop a technique for the description of the higher limits over categories of presentations and show that certain homological functors can be described in this way. In particular, we give a description of Hochschild homology and the derived functors of tensor, symmetric and exterior powers in the sense of Dold and Puppe as higher limits.
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