Medial law

Not to be confused with the interchange law.

An binary operator \oplus : X \times X \to X on a set X satisfies mediality or the medial law just when the equation

  (a \oplus b) \oplus (c \oplus d) =
  (a \oplus c) \oplus (b \oplus d)

holds.

The medial law is a special case of the interchange law when the two binary operations are the same. In fact, in deep inference the name medial is used exactly for the interchange law.

References

• nLab entry