Editing Congruence relation (section)

=== General ===
The general notion of a congruence relation can be formally defined in the context of [[universal algebra]], a field which studies ideas common to all [[algebraic structures]].  In this setting, a [[binary relation|relation]] <math>R</math> on a given algebraic structure is called '''compatible''' if
: for each <math>n</math> and each <math>n</math>-ary operation <math>\mu</math> defined on the structure: whenever <math>a_1 \mathrel{R} a'_1</math> and ... and <math>a_n \mathrel{R} a'_n</math>, then <math>\mu(a_1,\ldots,a_n) \mathrel{R} \mu(a'_1,\ldots,a'_n)</math>.

A congruence relation on the structure is then defined as an equivalence relation that is also compatible.{{sfnp|ps=|Barendregt|1990|p=338|loc=Def. 3.1.1}}{{sfnp|ps=|Bergman|2011|loc=Sect. 1.5 and Exercise 1(a) in Exercise Set 1.26 (Bergman uses the expression ''having the substitution property'' for ''being compatible'')}}