7 papers
Saturated directed spaces and generalized clocks
Philippe Gaucher
We construct a Hausdorff saturated directed space whose directed path space between two distinct points has nontrivial fundamental group although the corresponding trace space is a…
Left properness of Moore flows
Philippe Gaucher
We introduce reparametrization categories with cuts. For every such category , the tensor product of two objectwise weak homotopy equivalences of -spaces…
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…