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

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

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 follo...

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Veröffentlicht in:Transactions of the American Mathematical Society. Series B 2020-03, Vol.7 (1), p.1-23
Hauptverfasser: Kasprowski, Daniel, Winges, Christoph
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Winges, Christoph
description 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.
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title Shortening binary complexes and commutativity of K-theory with infinite products
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