# 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.

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