Positive model structures for abstract symmetric spectra

TL;DR

This paper introduces a systematic method for constructing positive stable model structures for symmetric spectra within an abstract simplicial symmetric monoidal model category, utilizing localization techniques.

Contribution

It provides a general localization-based approach to develop positive stable model structures for symmetric spectra in abstract settings.

Findings

Established a localization method for positive stable model structures.

Applied the method to abstract simplicial symmetric monoidal model categories.

Facilitated the construction of stable model structures via truncation and stabilization.

Abstract

We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category. The method is based on systematic localization, in Hirschhorn's sense, of a ceratin positive projective model structure on spectra, where positivity basically means the truncation of the zero slice. The localization above is by the set of stabilizing morphisms, or their truncated version.