Higher Segal structures in algebraic $K$-theory

TL;DR

This paper develops higher-dimensional analogues of classical simplicial constructions to produce algebraic K-theory spectra, exploring their fibrancy properties within the framework of higher Segal spaces.

Contribution

It introduces novel higher Segal structures in algebraic K-theory and analyzes their fibrancy, extending classical constructions to higher dimensions.

Findings

Established higher Segal analogues for K-theory spectra

Analyzed fibrancy properties of these higher structures

Extended simplicial constructions to higher dimensions

Abstract

We introduce higher dimensional analogues of simplicial constructions due to Segal and Waldhausen, respectively producing the direct sum and algebraic $K$-theory spectra of an exact category. We then investigate their fibrancy properties, based on the formalism of higher Segal spaces by Dyckerhoff-Kapranov.