Behavioural Equivalence

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<definition id="behavioural-equivalence">

 Suppose that C is a category with pullbacks and [math]F : \mathbf{C} \to \mathbf{C}[/math] a functor. Let [math]c : X \to F X[/math] and [math]d : Y \to F Y[/math] be coalgebras in C. If there is a cospan [math](X, c) \xrightarrow{h_1} (Z, e) \xleftarrow{h_2} (Y, d)[/math] in [math]\mathrm{Coalg}(F)[/math], then we say that the pullback [math]h_1 \times_Z h_2[/math] is a behavioural equivalence or kernel bisimulation for c and d.

</definition>

TODO:

  • Compare to bisimilary and other notions. See [1]

References

  1. Sam Staton, Relating Coalgebraic Notions of Bisimulation.