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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