?? toric correspondence ... ??? ... ??? doctrinal approach ??? ...???? ....
??? flat vs non-flat ??? .... ??? also in non-toric case ???... ???? abelian cats as forming an abelian-ish 2-cat .... ???? .....
?? reconstruct original level from correspondence level ... ??? .... ?? in special situations ... ?? ... ??? toric and / or non-toric ??? .....
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