6 papers
Left properness of Moore flows
Philippe Gaucher
We introduce the notion of a reparametrization category with cuts. For every such reparametrization category , we prove the tensor lemma, namely that the tensor product…
The q-model category of multipointed d-spaces is not left proper
Philippe Gaucher
We prove that the q-model category of -multipointed d-spaces for is not left proper by constructing a weak equivalence whose pu…
The chain replacement of a poset flow
Philippe Gaucher
We introduce the chain replacement of a poset flow: it is obtained by considering the simplicial nerves of the posets of strictly increasing chains in the given poset, ordered by r…
Branching spaces of transverse sets
Philippe Gaucher
A c-direct category is a small category equipped with an ordinal degree function such that every morphism is level or degree-raising. Every c-direct category is c-Reedy. The c-Reed…
Regular clock maps and trace spaces
Philippe Gaucher
A regular clock map is a regular map of directed spaces from a saturated directed space to the directed circle. We prove that the category of regular clock maps is a small-orthogon…
Directed paths and Moore flows
Philippe Gaucher
This addendum extends prior work to the non-regular setting by introducing the tame realization of a precubical set as a multipointed -space. Its execution paths are precisely t…