???so... the 3 models of the accidental topos of the projective line should be, from the viewpoint of the toric quasicoherent sheaves as the triples (a,b,c) with a and b N-sets and c a Z-equivariant anti-isomorphism between their tensor products with Z .... :

1 "take the underlying set of a" ...???

2 "take the underlying set of the common Z-set of a and b ..." ... ???...

3 "take the underlying set of b"


so ... are these models "representable" by a formula ??? .... ??? ....
??or maybe "tensor-representable" ??? ....????

??the two "affine" ones are representable by formula ??? ... but not the non-affine one ???? ... ???does that actually make sense??? ???not quite ??? ...