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

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.

23 pages

References in corpus (1)

• Algebraic K-theory of stable $\infty$-categories via binary complexes

Cited by in corpus (1)

• Vanishing of Nil-terms and negative K-theory for additive categories