Extend assembler and homological methods to higher K-groups

Investigate how to analogously extend Zakharevich’s Assembler-based methods for describing K1 (On K1 of an Assembler, J. Pure Appl. Algebra 2017) and the homological approach of Kupers–Lemann–Malkiewich–Miller–Sroka (Scissors automorphism groups and their homology, arXiv:2408.08081) to characterize the higher K-groups K_n(V_k) and, more generally, K_n(C) for pCGW categories, in a manner comparable to the extension of exact-category methods to pCGW categories developed here.

Background

The paper shows that techniques inspired by Nenashev and Grayson for exact categories can be adapted to pCGW categories to present K1 and suggests that similar adaptations should exist for higher K-groups.

However, the authors note that methods based on Assemblers and recent homological proofs have a different flavor and structure, and it is not straightforward to carry them over to the pCGW context for K_n with n>1.