This paper is devoted to connections between trace monoids and cubical sets. We prove that the category of trace monoids is isomorphic to the category of generalized tori and it is a reflective subcategory of the category of cubical sets. Adjoint functors between the categories of cubical sets and trace monoid actions are constructed. These functors carry independence preserving morphisms in the independence preserving morphisms. This allows us to build adjoint functors between the category of weak asynchronous systems and the category of higher dimensional automata.

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adjoint functors cubical sets reflective subcategory of generalized tori category of weak asynchronous systems of higher dimensional automata independence morphisms trace monoid actions

Ahmet A. Husainov,.Cubical Sets and Trace Monoid Actions. 2013 (),.

Ahmet A. Husainov,"Cubical Sets and Trace Monoid Actions" 2013

Ahmet A. Husainov,"Cubical Sets and Trace Monoid Actions"