English

A Hurewicz Model Structure for Directed Topology

Algebraic Topology 2021-02-03 v3 Category Theory

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.

Keywords

Cite

@article{arxiv.1911.02204,
  title  = {A Hurewicz Model Structure for Directed Topology},
  author = {Sanjeevi Krishnan and Paige Randall North},
  journal= {arXiv preprint arXiv:1911.02204},
  year   = {2021}
}

Comments

18 pages. minor clarifications, typos, and fixes. updated abstract. reworded section 6.5 and conclusion a bit for clarity

R2 v1 2026-06-23T12:07:01.495Z