A Hurewicz Model Structure for Directed Topology

TL;DR

This paper develops a new model structure for directed topology using streams and preordered spaces, extending classical fibrations and cofibrations, with applications to safety verification in database protocols.

Contribution

It introduces an h-model structure for diagrams of streams, extending classical characterizations of fibrations and cofibrations in directed topology.

Findings

Extended classical Hurewicz fibration characterizations.

Established a long exact sequence for directed homotopy monoids.

Applied the model to safety verification in database protocols.

Abstract

This paper constructs an h-model structure for diagrams of streams, locally preordered spaces. Along the way, the paper extends some classical characterizations of Hurewicz fibrations and closed Hurewicz cofibrations. The usual characterization of classical closed Hurewicz cofibrations as inclusions of neighborhood deformation retracts extends. A characterization of classical Hurewicz fibrations as algebras over a pointed Moore cocylinder endofunctor also extends. An immediate consequence is a long exact sequence for directed homotopy monoids, with applications to safety verifications for database protocols.