Higher Segal structures in algebraic $K$-theory

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.

arXiv comment25 pages

References in corpus (4)

• Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
• Higher categorical aspects of Hall Algebras
• Stable real K-theory and real topological Hochschild homology
• Hall monoidal categories and categorical modules

Cited by in corpus (11)

• Simplicial structures in higher Auslander-Reiten theory
• The symplectic geometry of higher Auslander algebras: Symmetric products of disks
• The incidence comodule bialgebra of the Baez-Dolan construction
• Comparison of Waldhausen constructions
• Lagrangian Cobordisms in Liouville manifolds
• Weak cartesian properties of simplicial sets
• Equivariant motivic Hall algebras
• Higher symmetries in abstract stable homotopy theories
• The bivariant parasimplicial ${\mathsf{S}}_{\bullet }$-construction
• Higher Auslander algebras of type $\mathbb{A}$ and the higher Waldhausen $S$-constructions
• Higher Segal spaces and Lax ${\mathbb{A}}_{\infty }$-algebras