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Antihomomorphism : ウィキペディア英語版
Antihomomorphism

In mathematics, an antihomomorphism is a type of function defined on sets with multiplication that reverses the order of multiplication. An antiautomorphism is a bijective antihomomorphism, i.e., an antiisomorphism, from a set to itself. From being bijective it follows that it has an inverse, and that the inverse is also an antiautomorphism.
==Definition==
Informally, an antihomomorphism is map that switches the order of multiplication.
Formally, an antihomomorphism between ''X'' and ''Y'' is a homomorphism \phi\colon X \to Y^} equals ''Y'' as a set, but has multiplication reversed: denoting the multiplication on ''Y'' as \cdot and the multiplication on Y^} is called the opposite object to ''Y''. (Respectively, opposite group, opposite algebra, opposite category etc.)
This definition is equivalent to a homomorphism \phi\colon X^} and acting as the identity on maps is a functor (indeed, an involution).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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