Dear Peter From memory, Bourbaki uses the term "chaotic" for the right adjoint to the forgetful Top --> Set. Since the left adjoint assigns the discrete topology, John Kelley used the term "indiscrete" (as a bit of a joke I thought; maybe because it indiscreetly defies separation properties) for the right adjoint. It is natural to use the same terms (discrete, and chaotic or indiscrete) for the adjoint to ob : Cat --> Set. I consider it one of those cultural things: the French use "chaotic", the Americans use "indiscrete", and I am happy with and have used both with a slight preference for "chaotic". Who used it first for categories would be hard to trace since the Top / Cat analogy runs long and deep. Regards, Ross On 29/09/2011, at 11:35 AM, 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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