What is "abstract nonsense"

n. 1 (context mathematics humorous English) Details which are straightforward but so tedious that an author or lecturer would rather skip them (especially those of a category theoretical nature). 2 (context mathematics humorous English) Details which involve diagram chasing. 3 (context mathematics humorous English) category theory in general.

In mathematics, abstract nonsense, general abstract nonsense, and general nonsense are terms used facetiously by some mathematicians to describe certain kinds of arguments and methods related to category theory. (Very) roughly speaking, category theory is the study of the general form of mathematical theories, without regard to their content. As a result, a proof that relies on category theoretic ideas often seems slightly out of context to those who are not used to such abstraction, sometimes to the extent that it resembles a comical non sequitur. Such proofs are sometimes dubbed “abstract nonsense” as a light-hearted way of alerting people to their abstract nature.

More generally, “abstract nonsense” may refer to any proof (humorous or not) that uses primarily category theoretic methods, or even to the study of category theory itself. Note that referring to an argument as "abstract nonsense" is not supposed to be a derogatory expression, and is actually often a compliment regarding the generality and sophistication of the argument.