  In \cite[Rem. 3.4]{DNO} the authors asked the question if any \'etale
subalgebra of an \'etale algebra in a braided fusion category is also \'etale.
We give a positive answer to this question if the braided fusion category $\cc$
is pseudo-unitary and non-degenerate. In the case of a pseudo-unitary fusion
category we also give a new description of the lattice correspondence from
\cite[Theorem 4.10]{DMNO}. This new description enables us to describe the two
binary operations on the lattice of fusion subcategories.
