so given a functor from minimal algebraically closed fields of finite characteristic to vector spaces, we get a functor from finite fields to vector spaces by assigning to a finite field the corresponding "fixed subspace"... then we can push forward to a functor from finite sets to vector spaces... or something like that... and take the "generating function"...

this should be parallel (or something...) to: given a representation of z, we get representations of each z/n by taking the elements fixed under the action of n... so what was baez's description of the "zeta function of a z-set" as the generating function of a certain structure type? ...

so for example let's consider the functor assigning to a field the free vector space spanned by the square roots of -1 in it... and the quotient functor obtained by modding out the hopefully obvious subfunctor... or something like that... but for finite fields this splitting off goes negative ... ??or something like that??.... so the l-function here is really the generating function of a _virtual_ functor... ??or something like that??

??the progression from representation of z to representations of each z/n preserves direct sums??

(but not equalizers...???)

ok, there's a bunch of mistakes and confusion here... i'm going to try and clear some of it up...