More generally, "abstract nonsense" may refer to a proof that relies on category-theoretic methods, or even to the study of category theory itself.
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... [6]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.
[7] When an audience can be assumed to be familiar with the general form of such arguments, mathematicians will use the expression "Such and such is true by abstract nonsense" rather than provide an elaborate explanation of particulars.
Referring to a joint paper with Samuel Eilenberg that introduced the notion of a "category" in 1942, Saunders Mac Lane wrote the subject was 'then called "general abstract nonsense"'.