Subject: categories: Who said: General Abstract Nonsense
From: [email-masked]
Date: Sun, 17 May 1998 08:00:58 +0000

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: [email-masked]
     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" <[email-masked]>

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 <[email-masked]>
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: [email-masked] (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 <[email-masked]>
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
<italic>abstract nonsense</italic> ( the terminology is due to
Steenrod)."