ABSTRACT
Erratum, 11 July 2022: This is an updated version of the original paper [20] in which the notion of reparametrization category was incorrectly axiomatized. Details on the changes to the original paper are provided in the Appendix.
A reparametrization category is a small topologically enriched semimonoidal category such that the semimonoidal structure induces a structure of a semigroup on objects, such that all spaces of maps are contractible and such that each map can be decomposed (not necessarily in a unique way) as a tensor product of two maps. A Moore flow is a small semicategory enriched over the biclosed semimonoidal category of enriched presheaves over a reparametrization category. We construct the q-model category of Moore flows. It is proved that it is Quillen equivalent to the q-model category of flows. This result is the first step to establish a zig-zag of Quillen equivalences between the q-model structure of multipointed $d$-spaces and the q-model structure of flows.
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Cited by
[1] Philippe Gaucher, "Homotopy theory of Moore flows (I)", Compositionality 3, 3 (2021).
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