Shortening binary complexes and commutativity of $K$-theory with infinite products

Trans. Amer. Math. Soc. Ser. B 7 (2020), 1-23 We show that in Grayson's model of higher algebraic $K$-theory using binary acyclic complexes, the complexes of length two suffice to generate the whole group. Moreover, we prove that the comparison map from Nenashev's model for $K_1$ to Grayso...

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Bibliographic Details
Main Authors Kasprowski, Daniel, Winges, Christoph
Format Journal Article
LanguageEnglish
Published 25.05.2017
Subjects
Mathematics - K-Theory and Homology
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Summary:Trans. Amer. Math. Soc. Ser. B 7 (2020), 1-23 We show that in Grayson's model of higher algebraic $K$-theory using binary acyclic complexes, the complexes of length two suffice to generate the whole group. Moreover, we prove that the comparison map from Nenashev's model for $K_1$ to Grayson's model for $K_1$ is an isomorphism. It follows that algebraic $K$-theory of exact categories commutes with infinite products.
DOI:10.48550/arxiv.1705.09116