scheme :: YELLOW18:sch 1
AltCatStrLambda{ F₁() -> non empty set , F₂( object , object ) -> set , F₃( object , object , object , object , object ) -> object } :

ex C being non empty transitive strict AltCatStr st
( the carrier of C = F₁() & ( for a, b being Object of C holds <^a,b^> = F₂(a,b) ) & ( for a, b, c being Object of C 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) ) )

provided

A1: for a, b, c being Element of F₁()
for f, g being set st f in F₂(a,b) & g in F₂(b,c) holds
F₃(a,b,c,f,g) in F₂(a,c)