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Subject: Groups vs. groupoids (Pat Donaly)
Date: Mon, 14 Jul 2003 14:47:48 EDT
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To all category theorists:

While (partially) responding to Tom Leinster's 7/04 query regarding limit
preservation, a query of my own occurred to me: On pages 6 and 7 of Alain Connes'
book, "Noncommutative Geometry", he writes, "It is fashionable among
mathematicians to despise groupoids and to consider that only groups have an authentic
mathematical status, probably because of the pejorative suffix oid."
Professor Connes later cites the groupoid of states of the hydrogen atom in order to
eliminate the prejudice against groupoids, but, for group theorists, there is a
more direct way: Since Frobenius and/or Burnside adopted the concept of an
abstract group in order to consider general group actions and representations,
group theorists have been heavily involved in groupoids, whether they liked it
or not.

Is it generally understood by categorists that every group action---as a
comma category---is a groupoid?

Pat Donaly