scheme :: YELLOW18:sch 2
CatAssocSch{ F₁() -> non empty transitive AltCatStr , F₂( object , object , object , object , object ) -> object } :

F₁() is associative

provided

A1: for a, b, c being Object of F₁() st <^a,b^> <> {} & <^b,c^> <> {} holds
for f being Morphism of a,b
for g being Morphism of b,c holds g * f = F₂(a,b,c,f,g) and
A2: for a, b, c, d being Object of F₁()
for f, g, h being set st f in <^a,b^> & g in <^b,c^> & h in <^c,d^> holds
F₂(a,c,d,F₂(a,b,c,f,g),h) = F₂(a,b,d,f,F₂(b,c,d,g,h))