??so what about... ??from toric:non-toric::"accidental topos":"accidental abelian category", also toric:non-toric::"doctrine combining topos and tag theory...":"doctrine combining abelian category and ag theory" ?? ... and so forth ...

??something about this idea as seeming to mesh nicely with ...previous idea about ... ???... ??noticing how in certain cases quasicoherent sheaves over toric variety can be thought of as ... ??abelian group objects in topos of quasicoherent sheaves ??? .... or something ... ??... ... and so forth ... ??...

??so what about some concept of "quasi-abelian category" ?? ... parallel to "quasi-topos", not "quasi-coherent" ... ???... and so forth ... ???...

??something about .... "combined doctrine" here as involved in bit about "globalization..." and "both forgetful functors preserving weakimits" (or something ...) ??? ...