If $\mathcal{C}=(\mathcal{A},r,\mathcal{X})$ is a Chu space, we can define the biextensional collapse of $\mathcal{C}$ to be $(\hat{r}[A],r^\prime,\check{r}[X])$ where $r^\prime(\hat{r}(a),\check{r}(x))=r(a,x)$

That is, to name the rows of the biextensional collapse, we just use functions representing the actual rows of the original Chu space (and similarly for the columns). The effect is to merge indistinguishable rows and columns.

We say that two Chu spaces are equivalent if their biextensional collapses are isomorphic.