2-Segal sets from cuts of rooted trees

Abstract

The theory of 2-Segal sets has connections to various important constructions such as the Waldhausen $S_{\bullet }$-construction in algebraic $K$-theory, Hall algebras, and (co)operads. In this paper, we construct 2-Segal sets from rooted trees and explore how these applications are illustrated by this example.

28 pages, to appear in WIT IV proceedings