The Grothendieck group of a triangulated category
arXiv:2404.15800
Abstract
We give a direct proof of the following known result: the Grothendieck group of a triangulated category with a silting subcategory is isomorphic to the split Grothendieck group of the silting subcategory. Moreover, we obtain its cluster-tilting analogue.
added a new section to discuss the cluster-tilting analogue