Abstract nonsense

More generally, "abstract nonsense" may refer to a proof that relies on category-theoretic methods, or even to the study of category theory itself. Roughly speaking, category theory is the study of the general form, that is, categories of mathematical theories, without regard to their content. As a result, mathematical proofs that rely on category-theoretic ideas often seem out-of-context, somewhat akin to a non sequitur. Authors sometimes dub these proofs "abstract nonsense" as a light-hearted way of alerting readers to their abstract nature. Labeling an argument "abstract nonsense" is usually not intended to be derogatory, and is instead used jokingly, in a self-deprecating way, affectionately, or even as a compliment to the generality of the argument. Alexander Grothendieck was critical of this notion, and stated that: The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps... Certain ideas and constructions in mathematics share a uniformity throughout many domains, unified by category theory. Typical methods include the use of classifying spaces and universal properties, use of the Yoneda lemma, natural transformations between functors, and diagram chasing.