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Article Dans Une Revue Theory and Applications of Categories Année : 2009

Homotopical interpretation of globular complex by multipointed d-space

Résumé

Globular complexes were introduced by E. Goubault and the author in arXiv:math/0107060 to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CW-complex. We prove that there exists a combinatorial model category such that the cellular objects are exactly the globular complexes and such that the homotopy category is equivalent to the homotopy category of flows introduced in arXiv:math/0308054. The underlying category of this model category is a variant of M. Grandis' notion of d-space over a topological space colimit generated by simplices. This result enables us to understand the relationship between the framework of flows and other works in directed algebraic topology using d-spaces. It also enables us to prove that the underlying homotopy type functor of flows constructed in arXiv:math/0308063 can be interpreted up to equivalences of categories as the total left derived functor of a left Quillen adjoint.
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Dates et versions

hal-00495657 , version 1 (06-10-2021)

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Philippe Gaucher. Homotopical interpretation of globular complex by multipointed d-space. Theory and Applications of Categories, 2009, 22 (22), pp.588-621. ⟨hal-00495657⟩
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