4.4 Congruence

Congruence is an equivalent relation with respect to an operator. Let $L \subseteq X \times X$ be an equivalent relation. It is also a congruence with respect to an operator $\cdot$ if and only if $\forall (x,x'),(y,y') \in L: (x \cdot y, x' \cdot y') \in L$

One of the main application of congruence is modulo mathematics. This will be discussed in a later section.