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Bjørn Kjos-Hanssen
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Gossip about Grothendieck and distributive lattices

In Gian-Carlo Rota's Indiscrete Thoughts, there a list of mathematical gossip among which one reads:

[...] What would have happened [...] if Grothendieck had known the theory of distributive lattices?

So... What would have happened? (and/or: what did Rota think would have happened?)