Stable Frames in Model Categories

TL;DR

This paper introduces a stable analogue of cosimplicial frames in model categories, enriching homotopy categories and providing new perspectives on the smash product of spectra, aligning with existing models.

Contribution

It develops a stable framework for cosimplicial frames in model categories, offering a novel description of the smash product of spectra and connecting it with established models.

Findings

Enrichment of homotopy categories over the stable homotopy category

New description of the smash product of spectra

Identification of Boardman's smash product with newer models

Abstract

We develop a stable analogue to the theory of cosimplicial frames in model cagegories; this is used to enrich all homotopy categories of stable model categories over the usual stable homotopy category and to give a different description of the smash product of spectra which is compared with the known descriptions; in particular, the original smash product of Boardman is identified with the newer smash products coming from a symmetric monoidal model of the stable homotopy category.