Does anyone know if there exists a name in the literature for the data of
1) a class of objects,
2) for each pair of objects $(x, y)$ a set $hom(x, y)$
3) for each triple of objects $(x, y, z)$ a morphism of sets $hom(x, y) \times hom(y, z) \to hom(x, z)$.
I don't impose any conditions on this data (if I were to impose the usual associativity and identity axioms this would be the definition of a category).