Thanks so much Alexander! This is really great! I could find very little about this construction anywhere in the literature, but it seemed like something that should obviously be doable, or at least discussable.

@ToddTrimble maybe I should get back over there! Haven't been on the forum in a really long time, but I seem to be wading into more and more categorical stuff recently (e.g. categories of operators, multicategories, the above).

For instance, unless I'm mistaken, one immediately has problems even getting that this monoidal structure is closed?

@ZhenLin ah, so the closed property goes away?