1. If we restrict to a class of subfactors $(N \subset M)$ wherein all the factors are isomorphic, we easily see how to define an isomorphism $\cong_{1}$ of subfactors.   

2. But in general, it seems natural to have an isomorphism $\cong$ such that, **even if $P \not\simeq Q$**  :
$(P \subset P) \cong (Q \subset Q) $ or $(N\bar\otimes P \subset M\bar\otimes P) \cong (N \bar\otimes Q \subset M\bar\otimes Q) $ or anything else...  
  

> How to define the isomorphism of subfactors in general ?