It is relevant, because it means that while `|` may produce a disjoint union if its arguments are already disjoint, it is not guaranteed to produce a disjoint u

It is relevant, because it means that while `|` may produce a disjoint union if its arguments are already disjoint, it is not guaranteed to produce a disjoint union in the general case. Hence, my original comment had a point. As if that weren't enough, any talk about universal properties is utterly pointless as soon as object identities matter everywhere.