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Hello everyone, I am a newbie to the category theory. While reading some paper about infinite Galois theory, the 'anti-equivalence' of two categories showed up. Could anyone give me a 'good' explanation what this means? Thanks a lot.

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up vote 10 down vote accepted

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: , .

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