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Allegories and Collagories for Transformation of Graph Structures Considered as Coalgebras

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Book cover Relational and Algebraic Methods in Computer Science (RAMICS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10226))

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Abstract

Although coalgebras are widely used to model dynamic systems with infinite behaviours, they are actually also a more natural tool than algebras to model the static systems that are the main subject of the “algebraic approach” to graph transformation and model transformation: many variants of graph structures and object webs are more easily modelled as coalgebras than as algebras. By characterising the kinds of coalgebras that give rise to different kinds of allegories, we make the tools of the relation-algebraic approach and also of the category-theoretic “adhesive” “algebraic approach” available to the transformations of coalgebras.

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Notes

  1. 1.

    Originally introduced as “I-functor” by Kawahara (1973).

  2. 2.

    These “check marks” indicate that the associated fact has a proof in the Agda development, with RATH-Agda theory location possibly visible in PDF readers supporting “tool tips”.

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Authors and Affiliations

  1. McMaster University, Hamilton, ON, Canada

    Wolfram Kahl

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  1. Wolfram Kahl
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Correspondence to Wolfram Kahl .

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Editors and Affiliations

  1. Data61, CSIRO, Sydney, New South Wales, Australia

    Peter Höfner

  2. CNRS, Lyon, France

    Damien Pous

  3. University of Sheffield, Sheffield, United Kingdom

    Georg Struth

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Kahl, W. (2017). Allegories and Collagories for Transformation of Graph Structures Considered as Coalgebras. In: Höfner, P., Pous, D., Struth, G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2017. Lecture Notes in Computer Science(), vol 10226. Springer, Cham. https://doi.org/10.1007/978-3-319-57418-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-57418-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57417-2

  • Online ISBN: 978-3-319-57418-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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