- Abstract nonsense
**Abstract nonsense**, or**general abstract nonsense**, alternatively**general nonsense**, is a popular term used bymathematician s to describe certain kinds of arguments and concepts incategory theory or applications.**History**The term predates the foundation of category theory as a subject itself. 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"'. [*Saunders Mac Lane. "The PNAS way back then". "Proc. Natl. Acad. Sci. USA" Vol. 94, pp. 5983–5985, June 1997.:"The first of these papers is a more striking case; it introduced the very abstract idea of a "category"—a subject then called "general abstract nonsense"!"*] The term is often used to describe the application of category theory and its techniques to less abstract domains. [*[*] [*http://www.csupomona.edu/~jis/1999/lord.pdf An Application of Abstract Nonsense to Surface Area*] , Harriet Lord*[https://www.cs.tcd.ie/~devriese/talks/cattheory.pdf Abstract Nonsense for Functional Programmers] , Edsko de Vries*]The term is believed to have been coined by the mathematician

Norman Steenrod , [*Colin McLarty, "The Uses and Abuses of the History of Topos Theory", Brit. J. Phil. Sci, 41 (1990) p 355. : "Steenrod jokingly tagged category theory 'abstract nonsense' and made it central to his axiomatics for homology"*] [*Joseph Rotman, "An Introduction to Homological Algebra", by Charles A. Weibel" (book review), Bull. Amer. Math. Soc., 33:4 (Oct. 1996) 473–476.:"The self-deprecating phrase "general abstract nonsense" (due to Steenrod) was promulgated by Eilenberg and Mac Lane, two of the major innovators of homological algebra, to highlight this aspect of the subject."*] himself one of the developers of the categorical point of view. This term is used by practitioners as an indication of mathematical sophistication (or possession of a deeper perspective) rather than as a derogatory designation. [*Michael Monastyrsky, "Some Trends in Modern Mathematics and the Fields Medal." Can. Math. Soc. Notes, March and April 2001, Volume 33, nos. 2 and 3. Online version available at http://www.fields.utoronto.ca/aboutus/FieldsMedal_Monastyrsky.pdf.:"In algebra, the term “abstract nonsense” has a definite meaning without any pejorative connotation."*]Certain ideas and constructions in mathematics display a uniformity throughout many domains. The unifying theme is category theory. When their 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. [

*MathWorld| urlname=AbstractNonsense | title=Abstract Nonsense*]**Examples**Typical instances are arguments involving

diagram chasing , application of the definition ofuniversal property , definition ofnatural transformation s betweenfunctor s, use of theYoneda lemma , arguments exploiting classifying spaces, and so on.To spell out a concrete example, consider a

3-manifold M with positiveBetti number . One would like to show that M admits a map to the 2-sphere which is "non-trivial", i.e. non-homotopic to the constant map. By a "general nonsense argument", there is a

$f:\; M\; o\; K(mathbb\{Z\},2)$ to theEilenberg-MacLane space , corresponding to a non-trivial element in H_{2(M). Since K(Z,2) is complex projective space and the latter admits a skeleton structure with no cells in odd dimensions, we can apply the cellular approximation theorem to conclude that the map "f" can be pushed down to the 2-skeleton, which happens to be the 2-sphere. Now surely there are more concrete, "hands-on" constructions of such a map, but the conceptual approach above would probably appeal to the elite.}**Notes and references****External links*** [

*http://www.math.harvard.edu/~elkies/M55a.05/nonsense.html Usage in mathematical exposition*] from [*http://www.math.harvard.edu/~elkies/ Noam Elkies' class notes*]

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**Abstract Nonsense**— est une expression anglaise utilisée en mathématiques pour décrire certains raisonnements et concepts en théorie des catégories. Le terme semble avoir été introduit par Steenrod[1]. Littéralement, elle signifie en français « abstraction… … Wikipédia en Français**Abstract nonsense**— est une expression anglaise utilisée en mathématiques pour décrire certains raisonnements et concepts en théorie des catégories. Le terme semble avoir été introduit par Norman Steenrod (en)[1]. À l origine, elle qualifie les raisonnements… … Wikipédia en Français**Abstract nonsense**— Die Kategorientheorie oder die kategorielle Algebra ist ein Zweig der Mathematik, der sich Anfang der 1940er Jahre zuerst im Rahmen der Topologie entwickelte; Saunders MacLane nennt seine 1945 gemeinsam mit Samuel Eilenberg entstandene „General… … Deutsch Wikipedia**abstract nonsense**— noun a) Details which are straightforward but so tedious that an author or lecturer would rather skip them (especially those of a category theoretical nature). b) Details which involve diagram chasing … Wiktionary**Nonsense (disambiguation)**— Nonsense is an utterance or written text that does not in fact carry any identifiable meaning. Nonsense may also mean: Abstract nonsense, a term used by mathematicians to describe certain kinds of arguments and concepts in category theory In… … Wikipedia**Nonsense**— For other uses, see Nonsense (disambiguation). For Wikipedia policy regarding nonsense, see Wikipedia:Patent nonsense. Nonsense is a communication, via speech, writing, or any other symbolic system, that lacks any coherent meaning. Sometimes in… … Wikipedia**Nonsense-Codon**— Als Stopcodon, auch Nonsense Codon wird in der Genetik ein Basentriplett (Codon) der Desoxyribonukleinsäure (DNA) beziehungsweise der Ribonukleinsäure (RNA) bezeichnet, für das keine zugehörige tRNA (Transfer RNA) vorliegt und somit den Abbruch… … Deutsch Wikipedia**List of mathematical jargon**— The language of mathematics has a vast vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject. Jargon often appears in… … Wikipedia**Mathematical jargon**— The language of mathematics has a vast vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject. Jargon often appears in… … Wikipedia**List of mathematics articles (A)**— NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A … Wikipedia