A higher limit approach to homology theories

Sergei O. Ivanov ^[1] ; Roman Mikhailov ^[1]
1. [1] St. Petersburg State University, Russia
Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 6 (June 2015), 2015, págs. 1915-1939
Idioma: inglés
DOI: 10.1016/j.jpaa.2014.07.016
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Resumen
- 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.