Antiisomorphism

In category theory, a branch of mathematics, an antiisomorphism (or anti-isomorphism) between structured sets A and B is an isomorphism from A to the opposite of B (or equivalently from the opposite of A to B).^[1] If there exists an antiisomorphism between two structures, they are said to be antiisomorphic.

Intuitively, to say that two mathematical structures are antiisomorphic is to say that they are basically opposites of one another.

The concept is particularly useful in an algebraic setting, as, for instance, when applied to rings.