4
$\begingroup$

In order for different kinds of objects (groups, algebras over a field, etc.) to have a nice uniform theory of representation you can use the notion of delooping as explained on the nLab.

Unfortunately this notion is completey inpenetrable to me using my current knowledge.

Is there an elementary definition of delooping?

In particular it should include the cases of groups and algebras over a ring, but preferably more kinds of interesting objects (Lie groups? Locally compact topological groups? I'm only guessing here since I'm not really familiar with those).

(Of course it is supposed to be "uniform", so no "case by case definition" is allowed)

  • 0
    The difference between a group and a groupoid is explained [here]( https://cornellmath.wordpress.com/2008/01/27/puzzles-groups-and-groupoids/) in elementary way. I also wonder if there is a similarly elementary explanation of delooping a group to a groupoid – 2018-07-01
  • 0
    @mma I know the difference between groups and groupoids. By 'elementary' I meant define it without resorting to fancy higher category theory, not 'explain it using it an example'. – 2018-07-01
  • 0
    As far as I see, such an alementary definition is also there. – 2018-07-01
  • 0
    @mma Again, that's not what I meant. Category theory is elementary to me (in the context of the question), higher category is not.- It's also unrelated since I'm *not* looking for the *definition of a groupoid*. I'm not even looking for the definition of delooping of a group. I'm looking for a fairly general *definition of delooping* of various objects which does not use higher categories. – 2018-07-01

0 Answers 0