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math.CT2026
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…
math.CT2026
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…
math.CT2026
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…
math.CT2026
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…