From: pareigis@math02.mathematik.uni-muenchen.de Date: Sun, 17 May 1998 08:00:58 +0000 Subject: categories: Who said: General Abstract Nonsense Hi - who coined the expression General Abstract Nonsense as a synonym for category theory? Where did it first appear in print? Thanks for any comments. Bodo -------------------------------------------------------------------- Prof. Dr. Bodo Pareigis Dept.of Mathematics, University of Munich Theresienstr. 39, D-80333 Muenchen, GERMANY ........................................... Email: pareigis@rz.mathematik.uni-muenchen.de Web: http://www.mathematik.uni-muenchen.de/~pareigis phone: office: +49 89-2394-4426 Date: Tue, 19 May 1998 18:34:33 +0100 Subject: Re: categories: Who said: General Abstract Nonsense From: "Tim Heap" pareigis writes: Bodo> Hi - who coined the expression Bodo> General Abstract Nonsense Bodo> as a synonym for category theory? Where did it first appear in Bodo> print? Lang, in his book `Algebra' says: "The terminology is due to Steenrod." tim Date: Tue, 19 May 1998 18:43:26 -0400 (EDT) From: Michael Barr Subject: categories: Re: Who said: General Abstract Nonsense This is interesting if indeed it was due to Steenrod. In that case, it was certainly not intended as a putdown (as Lang clearly intended it). Sammy Eilenberg told on a number of occasions the story that when General Theory of Natural Equivalences was published, Steenrod said that no paper had ever influenced his thinking more. He had been searching for years for an axiomatization of homology theory, but had never thought of using the induced homomorphisms as the basic tool. The result was, of course, the Eilenberg-Steenrod axioms. (The rest of the story is that P.A. Smith said he never read a more trivial paper in his life. Sammy commented that both reactions were valid.) On Tue, 19 May 1998, Tim Heap wrote: > pareigis writes: > > Bodo> Hi - who coined the expression > Bodo> General Abstract Nonsense > Bodo> as a synonym for category theory? Where did it first appear in > Bodo> print? > > Lang, in his book `Algebra' says: > "The terminology is due to Steenrod." > > tim > Date: Tue, 19 May 1998 17:30:31 -0700 From: peter@galois.geg.mot.com (Peter White) Subject: categories: Re: Who said: General Abstract Nonsense A quote from a Colin McLarty posting on another list: " Norman Steenrod first hung this tag on category theory. He had spent years trying to axiomatize homology, encouraged by Solomon Lefschetz. Lefschetz had also backed the young topologist Sammy Eilenberg, and encouraged Eilenberg's collaboration with the algebraist Mac Lane explicating certain calculations in homology. When Eilenberg and Mac Lane created category theory, Steenrod saw he could use their way of emphasizing morphisms at least as much as objects. He happily said this "abstract nonsense" was the key to solving his problem. The phrase was popularized by Lang's ALGEBRA, which had an index entry under "abstract nonsense". The page numbers sent you to various one line proofs such as "By abstract nonsense, tensor products are unique up to isomorphism when they exist". The joke got old and survives only vestigially in the latest edition." Peter White On Tue, May 19th, Michael Barr wrote: > > This is interesting if indeed it was due to Steenrod. In that case, it > was certainly not intended as a putdown (as Lang clearly intended it). > Sammy Eilenberg told on a number of occasions the story that when General > Theory of Natural Equivalences was published, Steenrod said that no paper > had ever influenced his thinking more. He had been searching for years > for an axiomatization of homology theory, but had never thought of using > the induced homomorphisms as the basic tool. The result was, of course, > the Eilenberg-Steenrod axioms. (The rest of the story is that P.A. Smith > said he never read a more trivial paper in his life. Sammy commented that > both reactions were valid.) > Date: Tue, 19 May 1998 20:16:08 -0400 From: John Duskin Subject: categories: Nonsense It might be amusing for people to see the full context as I replied to Bodo: Serge Lang used it in his Addiison-Wesley text: " Algebra" in the first(?) 1965 edition. On page 105 after the chapter on Homology, the following appears: "EXERCISES: Take any book on homological algebra, and prove all the theorems without looking at the proofs given in that book. Homological algebra was invented by Eilenberg-Mac Lane. General category theory (i.e. the theory of arrow-theoretic results ) is generally known as abstract nonsense ( the terminology is due to Steenrod)."