2018/12/12 by Cameron Calk, Calk, Cameron, Éric Goubault +3 · 1 citation
Computer Science · #18D35 #55U99 #68Q85 #Algebraic Topology (math.AT) #Category Theory (math.CT) #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Formal Methods in Verification #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Parallel #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.1812.05062
openalex publication_date 2018/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Directed topology was introduced as a model of concurrent programs, where the flow of time is described by distinguishing certain paths in the topological space representing such a program. Algebraic invariants which respect this directedness have been introduced to classify directed spaces. In this work we study the properties of such invariants with respect to the reversal of the flow of time in directed spaces. Known invariants, natural homotopy and homology, have been shown to be unchanged under this time-reversal. We show that these can be equipped with additional algebraic structure witnessing this reversal. Specifically, when applied to a directed space and to its reversal, we show that these refined invariants yield dual objects. We further refine natural homotopy by introducing a notion of relative directed homotopy and showing the existence of a long exact sequence of natural homotopy systems.