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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Katsumata, Sy., Sato, T. (2013). Preorders on Monads and Coalgebraic Simulations. In: Pfenning, F. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2013. Lecture Notes in Computer Science, vol 7794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37075-5_10
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