Subject: categories: Cohn obit

From: Peter Freyd <[email-masked]>
Date: Fri, 7 Jul 2006 10:49:54 -0400 (EDT)

[MathSciNet lists 29 items (out of almost 200) by Paul Cohn that are coded
  for categories. I've appended Fred Linton's review of one of his earlier
  categorical papers.]

                    Copyright 2006 Times Newspapers Limited
                               The Times (London)

                            June 29, 2006, Thursday

SECTION: FEATURES; Pg. 64

LENGTH: 425 words

HEADLINE: Professor Paul Cohn

BODY:

Professor Paul Cohn, FRS, mathematician, was born on January 8, 1924. He died on
April 20, 2006, aged 82.

Mathematician who devoted himself to algebra.

PAUL COHN was a distinguished algebraist and the former Astor Professor of
Mathematics at University College London.

An only child, he was born in Hamburg in 1924 to Jewish parents. At 15 he was
sent to England on the Kindertransport, and never saw the rest of his family
again.

After four years' manual labour, during which he taught himself Latin, he won an
exhibition to Trinity College, Cambridge, in 1944. He obtained his BA in 1948
and his PhD, working with Philip Hall at Cambridge, in 1951. After a year as a
charge de recherches at the University of Nancy, he served as a lecturer in the
University of Manchester (whose mathematics department rivalled that of
Cambridge in the early postwar years) from 1952 to 1962.

The rest of his career was in London: as Reader at Queen Mary College, 1962 67,
and as professor and head of department at Bedford College, 1967-84. The funding
cuts of the early 1980s led to the closure of the small colleges of the
University of London. Cohn left the Regent's Park campus of Bedford College for
University College, where he was Astor Professor from 1986 till his retirement
in 1989.

In addition to many visiting appointments he was elected Fellow of the Royal
Society in 1980, and served as president of the London Mathematical Society,
1982-84.

Cohn was a pure mathematician, whose extensive work was devoted to algebra. His
particular speciality was ring theory -the study of mathematical structures in
which, as with ordinary numbers, one can add, subtract and multiply, but not
necessarily divide -and in particular, non-commutative ring theory. Here, the
order in which one multiplies matters, unlike multiplication of ordinary
numbers, but as with the multiplication of matrices.

Cohn wrote nearly 200 mathematical papers, over more than 50 years. He also
wrote ten books, including the classic Algebra -this appeared first as two
volumes (1974-77), split into three (1982-91), and finally reappeared as two
again Basic Algebra and Further Algebra (2003). His best-known research
monograph was Free Rings and Their Relations (1971).

Cohn wrote on number theory as well as his beloved algebra, and was at home in
French, German and Russian.

He read widely and developed a particular interest in German history, the
background to his early troubles, of which he would talk freely.

He married Deirdre Sonia Sharon in 1958; she survives him, with their two
daughters.

     **********************************************************************

Cohn, P. M.
Morita equivalence and duality.
Queen Mary College Mathematics Notes
Queen Mary College, London, 1968 ii+79 pp.

These notes provide an introduction to, and an exposition of, the ideas of
Morita, Bass, Chase, Schanuel, et al., regarding the question, to be answered in
terms of the ground ring, of what module categories are equivalent, respectively
dual, to each other. The main goal is to provide a good presentation of the
equivalence theory; to this end, the notes of Hyman Bass ["The Morita theorems",
mimeographed notes, Univ. of Oregon, Eugene, Ore., 1962; see also Algebraic
$K$-theory, Chapter II, Benjamin, New York, 1968; MR0249491 (40 \#2736)] are
relied upon fairly heavily. A preliminary goal is to develop enough category
theory to get by with; the development is in fact very rapid, though not too
sketchy, but a little misleading or garbled in places (examples: the functor of
the exercise on page 8 is contravariant and goes elsewhere than is there stated;
the first two examples of equivalences of categories, presented on page 7 after
a brief sermon on the advantages of the notion of equivalence over that of
isomorphism, turn out, despite the readily inferred implication to the contrary,
to be in fact isomorphisms; the choice of the term "homotopy inverse" to
describe an inverse equivalence seems ill advised). A subsidiary goal is the
duality question, which receives an adequately careful treatment and is used to
open up the related area of quasi-frobeniosity.

Reviewed by F. E. J. Linton