A Hurewicz model structure for directed topology

Sanjeevi Krishnan and Paige Randall North

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.

Keywords: model structure, directed topology, Moore paths

2020 MSC: 18N40, 55P05

Theory and Applications of Categories, Vol. 37, 2021, No. 20, pp 613-634.

Published 2021-06-08.


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