_N-set_ as TAG theory ... ?? "every object as colimit of unit object" ??? ... ?? = "no stuff" ?? ....

?? whereas with explosion, "torus object" as maybe (?? "a priori" ... ?? ...) giving some stuff??? .... ????? ...... ???? .....

?? category where an object is a commutative monoid and a morphism is a functor between the cocone categories of their affine fans ... ???

hmm, that as adequate way to say only in "torsion-free" case ?? ... ??? ... ?? "direct limit of principal actions" ??? ... ????...

(non-toric analog?? ...)

hmm, so let's try homming N into N here .... ???? or N into the multiplicative monoid of a nice field ... ??? ...

??? hmmm, but what about symmetric monoidalness here??

??? "endomorphism e of 1, tw idempotent (??...) object on which e is invertible" .. ???....