:: deftheorem defines semi-functional ALTCAT_1:def 12 :
for C being non empty AltCatStr holds
( C is semi-functional iff for a1, a2, a3 being Object of C st <^a1,a2^> <> {} & <^a2,a3^> <> {} & <^a1,a3^> <> {} holds
for f being Morphism of a1,a2
for g being Morphism of a2,a3
for f9, g9 being Function st f = f9 & g = g9 holds
g * f = g9 * f9 );