Abstract nonsense

In mathematics, under the designation of general nonsense (English abstract nonsense or general nonsense ) summarized evidence that use abstract category theoretic arguments. The term is not pejorative to understand in general.

History

As birth of category theory is generally considered the 1942 published by Samuel Eilenberg and Saunders MacLane Work General Theory of Natural Equivalences. According to the theory of categories MacLane was then called by some people as a pejorative general abstract nonsense.

The popularization of the term with a non- pejorative meaning is now attributed to Norman Steenrod.

In the first two editions of the well-known algebra textbook by Serge Lang, there is an exercise:

" Homological algebra which invented by Eilenberg - MacLane. General category theory ( ie, the theory of arrow - theoretic results) is generated rally known as abstract nonsense (the terminology is due to Steenrod ). "

In the third edition of 1993, this task is missing, it is in the introduction to Part Four: homological algebra:

In the forties and fifties ( mostly in the works of Cartan, Eilenberg, MacLane, and Steenrod, see [ CAE 57 ] ), it what Realized thatthere was a systematic way of Developing Certain relationships of linear algebra, DEPENDING only on fairly general constructions Which were mostly arrow - theoretic, and were affectionately called abstract nonsense by Steenrod.

Examples

Typical examples include

• Evidence by chart hunts: a method of proof in homological algebra, which exploits the commutativity of diagrams, injectivity, surjectivity and bijectivity of morphisms or the exactness of sequences. An example is the construction of the connecting homomorphism in the proof of Schlangenlemmas.
• Use a universal property or adjoint functors.
• Applications of Lemma Yoneda.