(Co)homology of Spectral Categories

TL;DR

This paper develops (co)homology theories for spectral categories, reproduces model structures, and demonstrates their invariants' descent to stable $mbda$-categories along with a stabilization result.

Contribution

It introduces cotangent complex and (co)homology theories for spectral categories, extending their applicability and understanding.

Findings

Invariants descend to stable mbda-categories.

Established model structures on spectral categories.

Proved a stabilization theorem for spectral categories.

Abstract

In this article we develop the cotangent complex and (co)homology theories for spectral categories. Along the way, we reproduce standard model structures on spectral categories. As applications, we show that the invariants to descend to stable $\infty$-categories and we prove a stabilization result for spectral categories.