Strict refinement property of connected loop-free categories
Résumé
In this paper we study the strict refinement property for connected partial orders
also known as Hashimoto’s Theorem. This property implies that any isomorphism
between products of irreducible structures is determined is uniquely determined
as a product of isomorphisms between the factors. This refinement implies a
sort of smallest possible decomposition for such structures. After a brief recall
of the necessary notion we prove that Hashimoto’s theorem can be extended
to connected loop-free categories, i.e. categories with no non-trivial morphisms
endomorphisms. A special case of such categories is the category of connected
components, for concurrent programs without loops.
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