{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T23:40:08Z","timestamp":1762040408422,"version":"build-2065373602"},"reference-count":41,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2021,8,30]],"date-time":"2021-08-30T00:00:00Z","timestamp":1630281600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Compositionality"],"abstract":"<jats:p>Erratum, 11 July 2022: This is an updated version of the original paper \\cite{Moore1} 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 <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><\/mml:math>-spaces and the q-model structure of flows.<\/jats:p>","DOI":"10.32408\/compositionality-3-3","type":"journal-article","created":{"date-parts":[[2021,8,30]],"date-time":"2021-08-30T23:21:28Z","timestamp":1630365688000},"page":"3","source":"Crossref","is-referenced-by-count":3,"title":["Homotopy theory of Moore flows (I)"],"prefix":"10.46298","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0287-6252","authenticated-orcid":false,"given":"Philippe","family":"Gaucher","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris Cit\u00e9, CNRS, IRIF, F-75013, Paris, France"}]}],"member":"25203","published-online":{"date-parts":[[2021,8,30]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. Ad\u00e1mek and J. Rosick\u00fd. 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