@MISC{Pirashvili_simplicialdegrees, author = {Teimuraz Pirashvili}, title = {Simplicial Degrees Of Functors}, year = {} }

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Abstract

this paper is to show that if G is a simplicial group of finite length, then H n G also has finite length. Here the length of a simplicial group means the length of the corresponding Moore normalization and H n G is a simplicial abelian group given by [k] 7! H n G k . A similar fact is true if we replace G by a simplicial ring and we take the algebraic K-functors instead of group homology. The origin of such results goes back to the classical paper of Dold and Puppe (see Hilfsatz 4.23 of [DP]), where the following was proved: let