Magic Motives II
For instance, a vector space of dimension $n$ over a finite field may be represented by all $n$-tuplets of MUB operators representing the field. Now these tuplets are just collections of arrows in the category of fancy sets. A triplet of $3 \times 3$ matrices with cubed roots of unity would act on a $27$ element set, via Cartesian product. The collection of all finite dimensional vector spaces over $F_3$ would live in the set subcategory made up of Cartesian powers of the three element set.
Similarly, spaces for the two element field $F_2$ may occupy powers of the two element set, usually denoted by $\Omega$ in the ordinary topos. This suggests that a power set monad for fancy sets might have something to do with invariant functors for $F_2$ (or even $2$-adic numbers). How cool would that be? The world of motives would then return to Grothendieck's dream.