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Compositional Homomorphisms of Relational Structures

Modeled as Multialgebras
  • Michał Walicki
  • Adis Hodzic
  • Sigurd Meldal
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2138)

Abstract

The paper attempts a systematic study of homomorphisms of relational structures. Such structures are modeled as multialgebras (i.e., relation is represented as a set-valued function). The first, main, result is that, under reasonable restrictions on the form of the definition of homomorphism, there are exactly nine compositional homomorphisms of multialgebras. Then the comparison of the obtained categories with respect to the existence of finite limits and co-limits reveals two of them to be finitely complete and co-complete. Without claiming that compositionality and categorical properties are the only possible criteria for selecting a definition of homomorphism, we nevertheless suggest that, for many purposes, these criteria actually might be acceptable. For such cases, the paper gives an overview of the available alternatives and a clear indication of their advantages and disadvantages.

Keywords

Binary Relation Relational Structure Universal Algebra Categorical Property Partial Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Michał Walicki
    • 1
  • Adis Hodzic
    • 1
  • Sigurd Meldal
    • 2
  1. 1.Dept. of InformaticsUniversity of BergenBergenNorway
  2. 2.Dept. of CSCalPolySan Luis ObispoUSA

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