?? functoriality that we've been trying to exploit (?? to extract cartesian bi-stable categorified bialgebra from comm monoid ... ?? ...) as not quite right one ?? ...

?? instead we should probably try to use either contravariant ("functions" ... ?? ...) or covariant ("measures" ... ?? ...) version of ... ?? set-valued functors on "k(m,1)" ..... ???? .... ???? .....

(?? ... ??? not just "base change" but this extra level shift .... ???? .... ???? .... ?? recently wondered about things like this ... ?? ... ??? hint about unstable case ???? ..... ?? maybe instead of saying "base change" here i should say "choice of coefficients" ... ??? ... ?? realizing now that the level shift here seems strongly related to "hopf / bialgebra duality" ....?? slip vs flip ???? ... z vs z/2 ... ??? ... ?? bott periodicity ??? .... fourier duality ... hopf / bialgebra duality .... ??? .... 2 ... 8 ... 4 ... 2 ... ??? .....)

??? !! finish copying stuff from paper here .... !! ??? ...