Does the functor $X\times-:\mathbf{Loc}\to\mathbf{Loc}$ preserve small colimits for all locales $X$?
The reason that I'm interested in this question is that the same property fails in the category of topological spaces. If products preserve colimits in a total category then it must be cartesian closed. The category $\mathbf{Top}$ is total, but fails to be cartesian closed because products don't preserve colimits. So it would be curious if $\mathbf{Loc}$ failed to be cartesian closed for the complementary reason. It's not total, so maybe products do preserve colimits in $\mathbf{Loc}$?
Another reason to ask this question is that the definition of "locale" requires precisely that products preserve colimits in its frame of opens. So it would be interesting if this property was mirrored at the category level.