Lax functors and coalgebraic weak bisimulation

TL;DR

This paper extends coalgebraic weak bisimulation to lax functors, providing a categorical framework that unifies and generalizes existing notions, and applies it to timed systems.

Contribution

It introduces a new coalgebraic weak bisimulation based on lax functors, connecting saturation and adjunctions in a categorical setting.

Findings

The coalgebraic saturation can be expressed via lax functors.

The generalized weak bisimulation coincides with time-abstract behavioural equivalence.

The framework applies to timed systems, unifying their behavioral semantics.

Abstract

We generalize the work by Soboci\'nski on relational presheaves and their connection with weak (bi)simulation for labelled transistion systems to a coalgebraic setting. We show that the coalgebraic notion of saturation studied in our previous work can be expressed in the language of lax functors in terms of existence of a certain adjunction between categories of lax functors. This observation allows us to generalize the notion of the coalgebraic weak bisimulation to lax functors. We instantiate this definition on two examples of timed systems and show that it coincides with their time-abstract behavioural equivalence.