Category theory is post-modern algebra, analysing what may be inferred from the quite general observations about `morphisms' (which behave like functions) between `objects' (sets of values) which may be `composed'. Certain structural truths are presumed, based on some nominally naïve intuitions about the common ground shared by various mathematical structures which are amenable to description in such terms. From a carefully crafted small beginning of this kind, a great amount of structure may be built up within this model of the common ground, greatly improving our ability to see the underlying nature of the structures thus modelled - and the model is general enough to describe all mathematics, as far as I can make see.
I'm playing with kindred ideas so I've embarked on an attempt to describe structures such as category theory addresses, but using relations as my `implementation details' and playing with the structures that implementation suggests rather than slavishly following my limited knowledge of orthodox category theory. One thing I did learn: one can do away with `objects' in so far as each is entirely described by its identity morphism, and be left simply discussing composition of morphisms. Since the things I end up composing aren't introduced quite the way category theory introduces morphisms, I've called them something else: arrows.
I'll describe a binary operator, star = (:x-> (:y-> x*y :):), as an arrow land precisely iff