1 tangent / toric .... co-/tangent space of toric variety at point ... .... fano .... polytope .... ????? ......

2 level .... eckmann-hilton .... ????????? ...... loops and tails .... ????? x^a * x^b = x^a .... ??? ..... ??? category enriched over _semilattice_ ... vs semilattuce, also vs (??TAG??) topos ... ???? weak limits of syntactic categories, vs colimits in semantic categories ... ????? ....

3 ???flag .... "russian approach" ... direct sum of all irreps as multi-homogeneous coordinate algebra of flag variety .... ???? ... ???? relationship to toric stuff .... ???? ??? map ???? .... .... ???vs direct sum of all twisted tensor squares as coordinate alg of alg group itself .... ???? .... ...

4 comm monoid with "-1" that's not just free .... ????....

5 generalized lagrange extrapolation ....