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Article Dans Une Revue Compositionality Année : 2021

Homotopy theory of Moore flows (I)

Résumé

A reparametrization category is a small topologically enriched symmetric semimonoidal category such that the semimonoidal structure induces a structure of a commutative 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 closed 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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Dates et versions

hal-02989109 , version 1 (28-09-2021)
hal-02989109 , version 2 (26-12-2022)

Identifiants

Citer

Philippe Gaucher. Homotopy theory of Moore flows (I). Compositionality, 2021, 3 (3), ⟨10.32408/compositionality-3-3⟩. ⟨hal-02989109v1⟩
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