scheme :: ORDERS_3:sch 1
AltCatEx{ F1() -> non empty set , F2( object , object ) -> functional set } :
ex C being strict AltCatStr st
( the carrier of C = F1() & ( for i, j being Element of F1() holds
( the Arrows of C . (i,j) = F2(i,j) & ( for i, j, k being Element of F1() holds the Comp of C . (i,j,k) = FuncComp (F2(i,j),F2(j,k)) ) ) ) )
provided
A1: for i, j, k being Element of F1()
for f, g being Function st f in F2(i,j) & g in F2(j,k) holds
g * f in F2(i,k)