Preorders on Monads and Coalgebraic Simulations

  • Shin-ya Katsumata
  • Tetsuya Sato
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7794)

Abstract

We study the construction of preorders on Set-monads by the semantic ⊤ ⊤-lifting. We show the universal property of this construction, and characterise the class of preorders on a monad as a limit of a Card op -chain. We apply these theoretical results to identifying preorders on some concrete monads, including the powerset monad, maybe monad, and their composite monad. We also relate the construction of preorders and coalgebraic formulation of simulations.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Shin-ya Katsumata
    • 1
  • Tetsuya Sato
    • 1
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

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