On some new model category structures from old, on the same underlying category

TL;DR

This paper investigates the extension of existing model category structures, providing existence results, formal properties, and applications to enriched category homotopy theory.

Contribution

It introduces new existence theorems for ll-extensions of model categories and applies these to categories enriched over monoidal model categories.

Findings

Established conditions for the existence of ll-extensions.

Provided formal results about properties of ll-extensions.

Applied the theory to homotopy categories of enriched categories.

Abstract

We make a study of ll-extensions of model category structures. We prove an existence result of ll-extensions, present some specific and some rather formal results about them and give an application of the existence result to the homotopy theory of categories enriched over a monoidal model category.