  In this paper we study the strict refinement property for connected partial
ordersalso known as Hashimoto's Theorem. This property implies that any
isomorphismbetween products of irreducible structures is determined is uniquely
determinedas a product of isomorphisms between the factors. This refinement
implies asort of smallest possible decomposition for such structures. After a
brief recallof the necessary notion we prove that Hashimoto's theorem can be
extendedto connected loop-free categories, i.e. categories with no non-trivial
morphismsendomorphisms. A special case of such categories is the category of
connectedcomponents, for concurrent programs without loops.
