Ramana Kumar comments on Committing, Assuming, Externalizing, and Internalizing

[Ramana Kumar]

Similarly, for all $B\subset A$, $\left({\text{Commit}}^B\right(C){)}^{\ast }\cong {\text{Assume}}^B(C^{\ast })$ and $\left({\text{Commit}}^{\setminus B}\right(C){)}^{\ast }\cong {\text{Assume}}^{\setminus B}(C^{\ast })$.

We don’t need $B$ to be a proper subset here (i.e., I think $\subset$ is a typo for $\subseteq$). Also in my view all the isomorphisms in this section are actually equalities (but it’s also reasonable to never consider equality of frames).

[Scott Garrabrant]

Yeah, the $\subset$ was a typo, and I just never consider equality of frames.