Using Reedy techniques, this paper gives a correct proof of the left properness of the q-model structure of flows. It fixes the preceding proof which relies on an incorrect argument. The last section is devoted to fixing some arguments published in past papers coming from this incorrect argument. These Reedy techniques also enable us to study the interactions between the path space functor of flows with various notions of cofibrations. The proofs of this paper are written to work with many convenient categories of topological spaces like the ones of k-spaces and of weakly Hausdorff k-spaces and their locally presentable analogues, the Δ-generated spaces and the Δ-Hausdorff Δ-generated spaces.
Keywords: d-space, flow, topological model of concurrency, combinatorial model category, enriched semicategory, enriched non-unital category, locally presentable category, left proper model category, Reedy category
2020 MSC: 55U35, 18C35, 18G55, 68Q85
Theory and Applications of Categories, Vol. 37, 2021, No. 19, pp 562-612.