Homotopy theory of Moore flows (I)

Erratum, 11 July 2022: This is an updated version of the original paper \cite{Moore1} in which notion reparametrization category was incorrectly axiomatized. Details on changes to are provided Appendix.A a small topologically enriched semimonoidal such that structure induces semigroup objects, all spaces maps contractible and each map can be decomposed (not necessarily unique way) as tensor product two maps. A Moore flow semicategory over biclosed presheaves category. We construct q-model flows. It proved it Quillen equivalent result first step establish zig-zag equivalences between multipointed d-spaces