?? so what _about_ "torically flat quasicoherent preseheaf over toric variety" ???? ....
??? property/structure confusion here ?????? ....... ?? hmmm .... cartesian monoidalness of functor as property, vs monoidalness of it as structure ??? ..... ???? ..... ... ??? .... ?? toric convolution as only "formerly cartesian" ??? .... ????? ......
??? vs toric quasicoherent sheaf ???? ...... ???? ..... ....
?? TAG morphism as generally _not_ flat (... ???? ... "cartesian-product-preserving" .... ???? .... ???? .... ?? equalizers .... ???? ....) ..... ???? .....so ..... ??? more suspicion about extent to which "toric convolution of hallmark of toric tannakian program" makes any sense .... ???? ..... ??? how (if at all ... ??? ...) preservation of toric convolution relates to "toric spectrum" .... ????? vs "flat spectrum" .... ????? ...... ?????? ......
??? still lots of confusion here .... ????? ......
???? .... ??? bialgebra ??? ...... ????? ...... ....
??? lax monoidalness ???? ...... ...
?? extremely restrictive for morphism from walking object AG theory to preserve toric convolution ????? ....... ????? ...... ????? ...... ?? "flat" .... ???? ... ???? ...
?? hmmm.... ??? f(x # y) vs f(x) # f(y) .... f(x # y -> x) .... ???? arbitrary functor between cartesian smc's as op-lax monoidal ??? .... ??? .... ??? not applicable here (?? ...) ??? ..... ???? ..... ??? ..... .... ??? ...
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