Quasi-weak equivalences in complicial exact categories

TL;DR

This paper introduces quasi-weak equivalences in exact categories, providing a new approach to delooping and conditions for trivial negative K-groups, advancing algebraic K-theory understanding.

Contribution

It defines quasi-weak equivalences in exact categories, linking them to delooping and negative K-group triviality, which is a novel theoretical development.

Findings

Quasi-weak equivalences enable delooping in exact categories.

The approach provides conditions for negative K-group triviality.

Advances understanding of algebraic K-theory in exact categories.

Abstract

We introduce a notion of quasi-weak equivalences associated with weak-equivalences in an exact category. It gives us a delooping for (idempotent complete) exact categories and a condition that the negative $K$-group of an exact category becomes trivial.