scheme :: YELLOW18:sch 5
CategoryLambdaUniq{ F₁() -> non empty set , F₂( object , object ) -> object , F₃( object , object , object , object , object ) -> object } :

for C1, C2 being non empty transitive AltCatStr st the carrier of C1 = F₁() & ( for a, b being Object of C1 holds <^a,b^> = F₂(a,b) ) & ( for a, b, c being Object of C1 st <^a,b^> <> {} & <^b,c^> <> {} holds
for f being Morphism of a,b
for g being Morphism of b,c holds g * f = F₃(a,b,c,f,g) ) & the carrier of C2 = F₁() & ( for a, b being Object of C2 holds <^a,b^> = F₂(a,b) ) & ( for a, b, c being Object of C2 st <^a,b^> <> {} & <^b,c^> <> {} holds
for f being Morphism of a,b
for g being Morphism of b,c holds g * f = F₃(a,b,c,f,g) ) holds
AltCatStr(# the carrier of C1, the Arrows of C1, the Comp of C1 #) = AltCatStr(# the carrier of C2, the Arrows of C2, the Comp of C2 #)