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.

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:

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.
- Pedro Resende,
*Quantales, finite observations and strong bisimulation*, Theor. Comp. Sci.**254**:1–2 (2001) 95–149, doi

Revised on March 19, 2014 06:52:48
by Zoran Škoda
(193.136.196.12)