A non-empty set G is said to be a groupoid relatively to a binary operation denoted by f
g, if for every ordered pair (a; b) of elements of G there is a unique element ab 2 G. A groupoid (G;
) is called a quasigroup if for every a; b 2 G the equations a
x = b and y
a = b have unique solutions. A quasigroup (G;
) is called a Ward quasigroup if it satis es the law (a
c)
(b
c) = a
b for all a; b; c 2 G. A quasigroup (G;
) is called a Cote quasigroup if it satis es the law a
(ab
c) = (c
aa)
b for all a; b; c 2 G. A groupoid (G;
) is called a Manin quasigroup if it satis es the law a
(b
ac) = (aa
b)
c for all a; b; c 2 G.