What ⊔ means
It marks a union that keeps the inputs distinct.
In sqcup notation, A ⊔ B keeps a tag showing whether each element came from A or B. If one value occurs in both inputs, it can appear twice, once with each tag. In category theory, a disjoint union of sets is called a coproduct.
What is the history of square cup notation?
The documented 1888 date belongs to ordinary cup and cap signs.
Mathematician Peano used ∪ for union and ∩ for intersection in 1888. That documents the ordinary cup and cap notation; it does not date ⊔ itself.
The square-cup operator is used in set theory, topology, algebra, and category theory when keeping the identity of each component matters.
Formal mathematical notation, especially when a construction must preserve which input an element came from.
Use ∪ for ordinary union; ⊔ signals a disjoint union or a construction that keeps input labels.
Don't confuse it with
1Questions people ask
1Why does ⊔ show as a box on some devices?
Because that device's fonts have no glyph for it. The character is still correct and still copies correctly — the box is a missing glyph, not a broken character.
How to type ⊔
⊔\2294Codes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.