Sign up ×  By "compatible" I mean, if $R$ is my relation and $+$
my operation, then if $aRb$ and $cRd$, then $(a+c)R(b+d)$. For
an congruence relation this is claimed, but also that $R$ must
be an equivalence relation, but there are relations, like $<$
that fulfill the first statement, but are not equivalence
relation's. Are there any terms for such relations and are they
studied in mathematics?  share|cite|improve this question You
have chosen the right word, compatible is a standard technical
term for the notion. –  André Nicolas Feb 1 '13 at 19:33  1
Answer 1  up vote 3 down vote accepted  ...are they studied in
mathematics?  Considering a functional relation $R$, the
compatability says, in functional notation: $R(a+c)=R(a)+R(c)$.
In other words, the function preserves that operation. Of course
we study examples of such relations all the time whenever we are
looking at homomorphisms!  If you're asking if relations in
general are studied this way, then maybe so. While searhing I
came across a paper by Saund