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On the topological structures of nets

  • Part 3: Categorical Aspects From Topology
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Categorical Methods in Computer Science With Aspects from Topology

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 393))

Abstract

In this paper net theory used in computer science is studied from a categorical point of view. It turns out that the category Net of nets (and suitable morphisms) is a universally topological category over the category C of pairs of disjoint sets (and suitable morphisms) such that products of final maps are final. Consequently, Net is a quasitopos with concrete powers. Furthermore, occurance nets are studied and it is shown that the full subcategory of Net, whose objects are all nets with unbranched conditions, is extremal epireflective in Net.

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References

  1. ADAMEK, J., HERRLICH, H.: Cartesian closed categories, quasitopoi and topological universes. In: Mathematical Foundations of Programming Semantics, pp. 20–41. Lect. Notes Comp. Sc. 239. Berlin-Heidelberg-New York-London-Paris-Tokyo: Springer 1986.

    Google Scholar 

  2. BEST, E. FERNANDEZ, C.: Notations and Terminology on Petri Net Theory. Arbeitspapiere der GMD 195. St. Augustin: Gesellschaft für Mathematik und Datenverarbeitung Bonn. 1986.

    Google Scholar 

  3. DREES, S., GOMM, D., PLÜNNECKE, H., REISIG, W., WALTER, R.: Bibliography of Net Theory. Arbeitspapiere der GMD 212. St. Augustin: Gesellschaft für Mathematik und Datenverarbeitung Bonn. 1986.

    Google Scholar 

  4. HERRLICH, H.: Universal Topology. In: Categorical Topology, pp. 223–281. Sigma Ser. Pure Math. 5. Berlin: Heldermann. 1984.

    Google Scholar 

  5. HERRLICH, H., STRECKER, G.E.: Category Theory. Boston: Allyn and Bacon. 1973.

    Google Scholar 

  6. MENU, J., PULTR, A.: On simply bireflective subcategories. Cahiers Topol Géom. Diff. 17, 187–201 (1976).

    Google Scholar 

  7. PETRI, C.A.: Kommunikation mit Automaten. Schriften des IIM Nr. 2. Bonn: Institut für Instrumentelle Mathematik. 1962.

    Google Scholar 

  8. PREUSS; G.: Theory of Topological Structures. Dordrecht-Boston-Lancaster-Tokyo: D. Reidel. 1988.

    Google Scholar 

  9. REISIG, W.: Petri Nets. EATCS Monographs on Theoretical Computer Science 4. Berlin-Heidelberg-New York-Tokyo: Springer. 1985.

    Google Scholar 

  10. WINSKEL, G.: Petri nets, morphisms and compositionality. In: Advances in Petri Nets 1985, pp. 453–477. Lect. Notes Comp. Sc. 222. Berlin-Heidelberg-New York-London-Paris-Tokyo: Springer 1986.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Mathematik I, Freie Universität Berlin, Arnimallee 3, D-1000, Berlin 33

    Gerhard Preuß

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  1. Gerhard Preuß
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H. Ehrig H. Herrlich H. -J. Kreowski G. Preuß

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© 1989 Springer-Verlag Berlin Heidelberg

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Preuß, G. (1989). On the topological structures of nets. In: Ehrig, H., Herrlich, H., Kreowski, H.J., Preuß, G. (eds) Categorical Methods in Computer Science With Aspects from Topology. Lecture Notes in Computer Science, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51722-7_20

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  • DOI: https://doi.org/10.1007/3-540-51722-7_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51722-1

  • Online ISBN: 978-3-540-46787-8

  • eBook Packages: Springer Book Archive

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