Abstract nonsense - Definition and Overview

Abstract nonsense is a popular term used by mathematicians to describe certain kinds of arguments and concepts in category theory. This term is believed to have been coined by the mathematician Norman Steenrod, himself one of the developers of the categorical point of view. This term is used by practitioners as an indication of mathematical sophistication or coolness rather than as a derogatory designation.

Certain ideas and constructions in mathematics display a uniformity throughout many domains. The unifying theme is category theory. Rather than enter an elaborate discussion on particulars of arguments, mathematicians will use the expression Such and such is true by abstract nonsense. Typical instances are arguments involving diagram chasing, application of the definition of universal property, definition of natural transformations between functors, use of the Yoneda lemma and so on.