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Journal Article

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

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Winges,  Christoph
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1090/btran/43
(Publisher version)

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Citation

Kasprowski, D., & Winges, C. (2020). Shortening binary complexes and commutativity of K-theory with infinite products. Transactions of the American Mathematical Society. Series B, 7, 1-23. doi:10.1090/btran/43.


Cite as: http://hdl.handle.net/21.11116/0000-0006-9261-7
Abstract
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.