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International Conference on Category Theory and Computer Science

CTCS 1991: Category Theory and Computer Science pp 261–281Cite as

Dataflow networks are fibrations

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 530))

Abstract

Dataflow networks are a paradigm for concurrent computation in which a collection of concurrently and asynchronously executing processes communicate by sending messages over FIFO message channels. In a previous paper, we showed that dataflow networks could be represented as certain spans in a category of automata, or more abstractly, in a category of domains, and we identified some universal properties of various operations for building networks from components. Not all spans corresponded to dataflow processes, and we raised the question of what might be an appropriate categorical characterization of those spans that are “dataflow-like.” In this paper, we answer this question by obtaining a characterization of the dataflow-like spans as split right fibrations, either in a 2-category of automata or a 2-category of domains. This characterization makes use of the theory of fibrations in a 2-category developed by Street. In that theory, the split right fibrations are the algebras of a certain doctrine (or 2-monad) R on a category of spans. For the 2-categories we consider, R has a simple interpretation as an “input buffering” construction.

Research supported in part by NSF Grant CCR-8902215.

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Authors and Affiliations

  1. Department of Computer Science, State University of New York at Stony Brook, 11794, Stony Brook, NY, USA

    Eugene W. Stark

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  1. Eugene W. Stark
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Editor information

David H. Pitt Pierre-Louis Curien Samson Abramsky Andrew M. Pitts Axel Poigné David E. Rydeheard

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© 1991 Springer-Verlag Berlin Heidelberg

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Stark, E.W. (1991). Dataflow networks are fibrations. In: Pitt, D.H., Curien, PL., Abramsky, S., Pitts, A.M., Poigné, A., Rydeheard, D.E. (eds) Category Theory and Computer Science. CTCS 1991. Lecture Notes in Computer Science, vol 530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013470

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  • DOI: https://doi.org/10.1007/BFb0013470

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54495-1

  • Online ISBN: 978-3-540-38413-7

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