Hello everyone, I am a newbie to the category theory. While reading some paper about infinite Galois theory, the 'antiequivalence' of two categories showed up. Could anyone give me a 'good' explanation what this means? Thanks a lot.
All it means that one of the categories is equivalent to the opposite of the other. Wikipedia has informative pages on opposites of categories and equivalences of categories: http://en.wikipedia.org/wiki/Opposite_%28category_theory%29 , 

