A Moufang loop is a loop A = (A,·,\,/,e) such that
((xy)z)x = x(y(zx)) and y(x(yz)) = ((yx)y)z and (yx)(zy) = (y(xz))y.
Let A and B be Moufang loops. A morphism from A to B is a function h : A→B that is a homomorphism: h(xy) = h(x)h(y) and h(x\y) = h(x)\h(y) and h(x/y) = h(x)/h(y) and h(e) = e.
|Congruence extension property|
|Definable principal congruences|
|Equationally definable principal congruences|
|Strong amalgamation property|
|Epimorphisms are surjective|