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High Quality Content by WIKIPEDIA articles! In category theory, weak n-categories are a generalization of the notion of (strict) n-category where composition is not strictly associative but only associative up to an isomorphism, which is itself associative up to an isomorphism, which is itself. There is currently much work to determine what the coherence laws should be for those. Weak n-categories have become the main object of study in higher category theory.