A Lax symmetric cubical category associated to a directed space (Q2839801)

\(d\)-spaces are topological spaces equipped with a distinguished set of continuous maps aimed at modelling non-reversible phenomena involving the direction of time. In this paper, the author introduces the lax symmetric cubical category of a \(d\)-space. It is a higher dimensional version of his notion of fundamental category. The singular cubes of a \(d\)-space assemble to a symmetric precubical category with the addition of transversal maps given by reparametrisations, invertible comparisons for pseudo associativity, comparisons for lax unitarity and identity comparisons for strict interchange. By a similar construction, the Moore cubes of a \(d\)-space give a strict symmetric cubical category.