Let be a category. A triangle of morphisms of consists of objects of and morphisms , , and . This is often pictured as a triangle
The triangle is commutative if .
A commutative triangle is determined entirely by and ; therefore, a commutative triangle is equivalent to a composable pair of morphisms.
Accordingly, one rarely hears of commutative triangles on their own; instead, the concept only comes up when one already has a triangle and asks whether it commutes. (This is different from the situation with commutative squares.)