A more general categorical framework for congruence of applicative bisimilarity

We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations on terms other than capture-avoiding substitution. This is typically the case for PCF, $\lambda$-calculus with delimited continuations, and early-style bisimilarity in higher-order process calculi.