In the pi calculus, there is an equivalence relation between terms that are structurally equivalent and should "act the same", which is usually described as structural congruence rules. For example, the reduction rules are usually described modulo the structural congruence.
My question is: in the context of a calculus, what exactly turns a relation as such into a congruence? Let's say I'm working with some process calculus, what would I need to prove in order to say that a similar equivalence relation is, in fact, a congruence?
