nLab
bisimulation

In Joyal-Nielsen-Winskel (p.13) is given the following definition. For what a “path category in a category of models” is, see there.

Definition

Let $P$ be a path category in a category of models $M$. Two objects $X_1,X_2$ are called to be $P$-bisimilar if there is a span of $P$-open maps $X_1\leftarrow X\to X_2$.

The relation of $P$-open maps and open maps is given by Proposition 11, p.32:

Proposition

If $P$ is a dense full subcategory of $M$, then $f$-is $P$-open iff $M(-,f)$ is an open map.

• Wikipedia (English), Bisimulation
• Sam Staton, Relating coalgebraic notions of bisimulation
• Davide Sangiorgi, On the Origins of Bisimulation and Coinduction
• André Joyal, Mogens Nielsen?, Glynn Winskel, Bisimulation from open maps, pdf
• Bard Bloom, Sorin Istrail, Albert Meyer, Bisimulation can’t be traced, pdf
• Yde Venema, Algebras and Coalgebras, §6 (p.332-426).11(p.398-403) in Blackburn, van Benthem, Wolter, Handbook of modal logic, Elsevier, 2007.