Suppose we have $u ; v ; w = id ; w$. Is it right to say that we also have $u ; v = id$?
I thought that this is like Leibniz, but the implication seems to be the wrong way round.
Suppose we have $u ; v ; w = id ; w$. Is it right to say that we also have $u ; v = id$?
I thought that this is like Leibniz, but the implication seems to be the wrong way round.
No, there's no reason you can cancel $w$. If $w$ is a morphism to a terminal object, for instance, then the equation automatically holds for all possible choices.of $u,v$.