Lower Right Corner With Dot

It declares that a square of arrows is a pullback.

Category theory is the branch of mathematics that studies objects and the maps (arrows) between them, and it reasons with diagrams of arrows. Take two maps that land in the same place, f: A → C and g: B → C. Their pullback collects every pair (a, b) with f(a) = g(b): everything from A and B that agrees once mapped into C. For ordinary sets this is the fibre product A ×_C B, a bit like joining two tables on a shared column.

In a diagram the pullback is the top-left corner of a square whose other corners are A, B and C. The mark sits just inside that corner, its right angle pointing at it, so a reader knows at a glance the square is not merely commutative but a pullback (also called a Cartesian square).

Where did the corner mark come from?

Peter Freyd recalled using a similar right-angle mark in lectures in 1974, and Paul Taylor's widely used package for drawing diagrams in LaTeX had it by 1994. No single inventor is credited.

In papers the mark is usually drawn without the dot, as ⌟, typed in LaTeX as \lrcorner. Unicode encodes the dotted ⟓ separately, together with its pushout partner ⟔.