Re: Reference requested

[Peter May <may@math.uchicago.edu>]

Thanks everybody for comments, although I guess the use
goes so far back into antiquity that the request for an original
reference is unanswerable.  For context, with two young
collaborators (Bertrand Guillou and Mona Merling), I
have a draft in progress tentatively entitled ``Chaotic
categories and equivariant classifying spaces''.

I prefer `chaotic' to `indiscrete' not just because
of the `coarse' implications of the latter, but because
indiscrete spaces are boring, `null or banal', whereas
chaotic categories have genuinely significant applications.
They are quite surprisingly central to the theory of universal
bundles, equivariant or not.

Via the (product-preserving) classifying space construction
from categories (especially categories internal to spaces)
to spaces, they provide a rich source of contractible spaces
that can very easily be given interesting additional structure.
That is just what one wants when constructing universal bundles.

More fun, it is just what one wants to construct an E infinity
operad of G-categories that defines `genuine' symmetric
monoidal G-categories (which are not merely symmetric
monoidal categories on which a group G acts in the obvious
`naive' way).   These which give rise to `genuine' G-spectra.
Genuine G-spectra that define equivariant algebraic K-theory
arise in precisely this way.    All starting from chaotic trivialities.


Cheers,

Peter


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