On a sequence of Grothendieck groups

Abstract

We show that a well-known exact sequence in K-theory for quotients of triangulated categories descends to numerical K-groups provided that the category, the quotient and the category we take the quotient with has a numerical K-group, and if either the quotient functor preserves compactness or the K-group of the quotient is torsion-free.

arXiv comment9 pages. Title was changed and a new application was added. Final version. To appear in Homology, Homotopy and Applications. arXiv admin note: text overlap with arXiv:2105.13334