Re: Reference requested

[Ronnie Brown <ronnie.profbrown@btinternet.com>]

Why not use the term `indiscrete groupoid' for the functor that gives a
right adjoint to the  functor Ob: Groupoids \to Sets?   The left adjoint
is then of course the `discrete groupoid'.  This agrees with the
terminology for discrete and indiscrete topologies.

I confess to have used different  terminology in various places.

Of course one use of these notions is to show that the functor Ob
preserves limits and colimits, which is  a start on constructing them.

It is not surprising that this concept occurs widely. In groupoids there
is a notion of covering morphism and the universal cover of a group G
is of course an indiscrete groupoid G'; this groupoid is by no means
`trivial' since it comes equipped with a covering morphism  p: G' \to
G.  This approach to covering space theory is given in my book `Topology
and groupoids'.

Ronnie



Ronnie

On 29/09/2011 02:35, Peter May wrote:
> I have a reference question.  Who first coined the term
> ``chaotic category'' for a groupoid with a unique morphism
> between each pair of object, and in what context?  It is a
> ridiculously elementary concept, but one that is extremely
> useful in  work on equivariant bundle theory that is needed
> for equivariant infinite loop space theory and equivariant
> algebraic K-theory.
>
> Peter May
>
>
>

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