48 citations · 356 across the 46 of their papers we have counts for
48 papers
Towards a theory of natural directed paths
Philippe Gaucher
We introduce the abstract setting of presheaf category on a thick category of cubes. Precubical sets, symmetric transverse sets, symmetric precubical sets and the new category of (…
Homotopy theory of Moore flows (III)
Philippe Gaucher
The previous paper of this series shows that the q-model categories of -multipointed -spaces and of -flows are Quillen equivalent. In this paper, the s…
Directed degeneracy maps for precubical sets
Philippe Gaucher
Symmetric transverse sets were introduced to make the construction of the parallel product with synchronization for process algebras functorial. It is proved that one can do direct…
Regular directed path and Moore flow
Philippe Gaucher
Using the notion of tame regular -path of the topological -cube, we introduce the tame regular realization of a precubical set as a multipointed -space. Its execution path…
Erratum to "Homotopy theory of Moore flows I"
Philippe Gaucher
The notion of reparametrization category is incorrectly axiomatized and it must be adjusted. It is proved that for a general reparametrization category , the tensor pr…
Comparing cubical and globular directed paths
Philippe Gaucher
A flow is a directed space structure on a homotopy type. It is already known that the underlying homotopy type of the realization of a precubical set as a flow is homotopy equivale…