On the cyclic homology of exact categories.(English)Zbl 0923.19004
R. McCarthy [J. Pure Appl. Algebra 93, No. 3, 251-296 (1994;Zbl 0807.19002)] defined the cyclic homology of an exact category. However, as it was shown by the author, that theory cannot be both compatible with localization and invariance under functors inducing equivalences.
That is the article’s motivation for defining a new theory for which these properties hold. Then that new theory is computed for a number of categories.
That is the article’s motivation for defining a new theory for which these properties hold. Then that new theory is computed for a number of categories.
Reviewer: M.Golasiński (Toruń)
MSC:
| 19D55 | \(K\)-theory and homology; cyclic homology and cohomology |
| 18E10 | Abelian categories, Grothendieck categories |
| 16E40 | (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
| 18E30 | Derived categories, triangulated categories (MSC2010) |
| 18F25 | Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) |
Keywords:
exact category;coherent sheaves;cyclic homology;derived category;localization pair;projective space;triangulated categoryCitations:
Zbl 0807.19002Cite
Full Text:DOI
References:
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