On abstractions of nets
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The central idea of General Net Theory is to emphasize morphisms between nets instead of studying single nets. The paper contributes to this theory and proposes a formalism for net transformations which is based on a subclass of surjective net morphisms, called abstractions.
Up to isomorphism, each abstraction of a net can be characterized by an equivalence relation on its elements. Feasible equivalence relations, which define abstractions, are characterized. They define quotient nets, analogously to quotients of sets. Some closure properties of feasible relations are studied.
Finally, it is shown that each abstraction can be decomposed into a folding (foldings are a known subclass of abstractions) and a simple contraction (which is a local transformation defined in the paper).
KeywordsNet morphisms transformations coarsening and composition of nets
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