preprint: Homotopy Theory of Labelled Symmetric Precubical Sets

preprint: Homotopy Theory of Labelled Symmetric Precubical Sets

[Philippe Gaucher]

Dear Categorists,

Any comment is welcome. pg.


Title: This paper is the third paper of a series devoted to higher dimensional
transition systems. It is proved that there exists a model category of
labelled symmetric precubical sets which is Quillen equivalent to the Bousfield
localization of the left determined model category of cubical transition
systems by the cubification functor. The realization functor from labelled
symmetric precubical sets to cubical transition systems is not a left Quillen
functor: it is only a left adjoint. It is proved that the two model categories
are related to each other by a zig-zag of Quillen equivalences of length two.
The class of cofibrations of this new model category structure is strictly
larger than the class of monomorphisms. The weak equivalences are closely
related to bisimulation. Similar results are obtained by restricting the
constructions to the labelled symmetric precubical sets satisfying the HDA
paradigm.

Url: http://www.pps.univ-paris-diderot.fr/~gaucher/HomotopyPrecubicalSet.ps
http://www.pps.univ-paris-diderot.fr/~gaucher/HomotopyPrecubicalSet.pdf


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