Monoidal Properties of Franke's Exotic Equivalence

TL;DR

This paper investigates the monoidal properties of Franke's reconstruction functor R, demonstrating its compatibility with monoidal products despite not being a tensor-triangulated functor, thus shedding light on exotic triangulated equivalences.

Contribution

It establishes that Franke's functor R, though not tensor-triangulated, still preserves monoidal structures, revealing new insights into exotic triangulated equivalences.

Findings

Franke's functor R is compatible with monoidal products.

R provides exotic triangulated equivalences not arising from Quillen equivalences.

The work clarifies the monoidal behavior of R in stable model categories.

Abstract

Franke's reconstruction functor R is known to provide examples of triangulated equivalences between homotopy categories of stable model categories, which are exotic in the sense that the underlying model categories are not Quillen equivalent. We show that, while not being a tensor-triangulated functor in general, R is compatible with monoidal products.