Two morphisms e: a -> b and m: x -> y are orthogonal iff for any (f, g) such that the square commutes:

a --e--> b|        |f        g|        |v        vx --m--> y

then there exists a UNIQUE diagonal d: b -> x such that the the triangles commute: ( f = d . e) and ( m . d = g):

a --e--> b|       / |f      / g|   /!d  |v /      vx --m--> y