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Communication Dans Un Congrès Année : 2008

A topological model for studying branching and merging homologies of flows

Philippe Gaucher

Résumé

There exist various methods for modeling time flows associated with concurrent systems. The study of the branching and merging homologies of a time flow requires a very specific feature: the mapping taking an object to its set of non-constant execution paths must be functorial. The first model I studied is the one of non-contracting Kan strict globular omega-categories consisting of the category of strict globular omega-categories C such that PC=C_1 U C_2 U ... is a strict omega-groupoid (hence the word ''Kan'', C_n being the set of n-morphisms) and of omega-functors f:C -> D inducing a map of strict omega-groupoids Pf:PC->PD (hence the word ''non-contracting''). The second model I studied is a version of the preceding model in which the path space PC is topologized, hence the notion of flows (small category without identities enriched over topological spaces). The third and last model I am studying now is a variant of M. Grandis' notion of d-space, the multipointed d-spaces, in which not only the path space is topologized, but also the direction of time. The three models are locally presentable, by working with Delta-generated spaces. The last one of multipointed d-spaces is also topological. In this talk, I will present the last model and its relation with the model of flows.
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Dates et versions

hal-00695198 , version 1 (07-05-2012)

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  • HAL Id : hal-00695198 , version 1

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Philippe Gaucher. A topological model for studying branching and merging homologies of flows. CONFÉRENCE INTERNATIONALE DE THÉORIE DES CATÉGORIES 2008, Jun 2008, Calais, France. ⟨hal-00695198⟩
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