Spaces of directed paths on pre-cubical sets II (Q2304017)

For a given precubical set \(K\) with two distinct vertices \(0\) and \(1\), the author proves that the space \(\vec{P}(K)_0^1\) of \(d\)-paths on the geometric realization of \(K\) with source \(0\) and target \(1\) is homotopy equivalent to its subspace \(\vec{P}'(K)_0^1\) of tame \(d\)-paths. When \(K\) is the underlying precubical set of a Higher Dimensional Automaton \(A\), tame \(d\)-paths on \(K\) represent step executions of \(A\). Then the author defines the cube chain category of \(K\) and proves that its nerve is weakly homotopy equivalent to \(\vec{P}(K)_0^1\).