The $K'$- theory of monoid sets

TL;DR

This paper develops the K-theory for categories of partially cancellative monoid sets, providing foundational results and example computations to better understand their algebraic structure.

Contribution

It introduces a K-theory framework for partially cancellative monoid sets using CGW-category formalism, advancing the understanding of their algebraic properties.

Findings

Established foundational results for the K-theory of monoid sets.

Demonstrated the improved behavior of partially cancellative monoid sets.

Provided numerous example computations illustrating the theory.

Abstract

This paper studies the K-theory of categories of partially cancellative monoid sets, which is better behaved than that of all finitely generated monoid sets. A number of foundational results are proved, making use of the formalism of CGW-categories due to Campbell and Zakharevich, and numerous example computations are provided.