Injective and Projective Model Structures on Enriched Diagram Categories

TL;DR

This paper establishes the existence of injective and projective model structures on enriched diagram categories under certain conditions, extending model category theory to enriched settings using advanced lifting techniques.

Contribution

It proves the existence of these model structures in enriched diagram categories, leveraging recent methods of lifting model structures from adjunctions.

Findings

Model structures exist on enriched diagram categories under specified conditions.

The approach uses lifting techniques from an adjunction framework.

Results extend classical model category theory to enriched contexts.

Abstract

In the enriched setting, the notions of injective and projective model structures on a category of enriched diagrams also make sense. In this paper, we prove the existence of these model structures on enriched diagram categories under local presentability, accessibility, and "acyclicity" conditions, using the methods of lifting model structures from an adjunction introduced by Garner, Hess, Kedziorek, Riehl, and Shipley.