Enriched diagrams of topological spaces over locally contractible enriched categories

TL;DR

This paper establishes a Quillen equivalence between the model structure of enriched diagrams over locally contractible categories and standard topological spaces, providing a geometric interpretation in directed homotopy.

Contribution

It introduces a new Quillen equivalence for enriched diagram categories over locally contractible categories, linking them to classical topological spaces.

Findings

Quillen equivalence between enriched diagram categories and topological spaces

Geometric interpretation in directed homotopy

Extension of model structures to enriched categories

Abstract

It is proved that the projective model structure of the category of topologically enriched diagrams of topological spaces over a topologically enriched locally contractible small category is Quillen equivalent to the standard Quillen model structure of topological spaces. We give a geometric interpretation of this fact in directed homotopy.