Simplicial radditive functors

TL;DR

This paper develops a framework to prove that simplicial extensions of certain functors preserve weak equivalences across various closed model categories, broadening the applicability of such results.

Contribution

It introduces a general framework for establishing weak equivalence preservation by simplicial functors in diverse closed model categories.

Findings

Framework applicable to a wide class of closed model categories

Conditions under which simplicial extensions preserve weak equivalences

Potential to unify and extend existing results in homotopical algebra

Abstract

The simplicial extension of any functor from Sets to Sets which commutes with directed colimits takes weak equivalences to weak equivalences. The goal of the present paper is construct a framework which can be used to proof results of this kind for a wide class of closed model categories and functors between those categories.