?? daydreaming about modular but non-distributive lattices ... trying to fit various ingredients together ....

1 ?? subgroup lattice of klein-4 ... ?? ...

2 ?? anecdote about von neumann and someone ... ?? maybe birkhoff ?? ... about ... ??? some free modular lattice ?? ... ??? construed as natural operations (?? ternary ?? ...) on vector subspaces ... ??? ..... numerology of it ... ?? ...

3 ?? stuff jeff egger said ... how the prototypical modular but non-distributive lattice shows up in understanding different flavors of duality ... ?? star-autonomous vs compact ?? ... ??? .... (??? at the moment a bit confused about egger's story because i was imagining that the self-duality of the prototypical example might cause a paradox ... but don't remember having that feeling at all during the discussion, so presumably it's ok ...) ... ?? some inequivalence between different tensor products or homs involving it .... ?? tensoring it with itself ... numerology .... ?? vaguely trying to connect with the von neumann numerology now ...

4 buildings ... distributive : modular :: q=1 : q#1 ... ???? segal and pressley ... ?? ... ?? birkhoff again ??? .....

5 ?? categorifying the prototypical example into "modular but non-distributive topos" ... ?? ...

6 recent ideas about absolute colimits and duality and so forth .... ag correspondences ... ??? .....

??? .....