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In Lawvere's article Comments on the Development of Topos Theory, the author writes:

Similarly, Grothendieck and others unerringly recognized which kinds of mathematical structures are 'preserved by all functors which preserve finite limits and arbitrary colimits'. (A very impressive list was produced by Grothendieck [47] during his 1973 stay in Buffalo; during the same visit he advocated the abandonment of his earlier complicated definition of 'scheme', but unfortunately the simpler alternative he offered does not seem to have found its way into the textbooks.)

The reference in the bibliography reads:

[47] A. Grothendieck, List of classes of structures, 1973 (now in J. Duskin's file.)

Can anyone direct me to a copy of this document? I haven't been able to find one.

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    $\begingroup$ I like your question, and I love your picture. $\endgroup$
    – Joël
    Commented Dec 19, 2015 at 16:24
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    $\begingroup$ And what's the simpler alternative definition of scheme? $\endgroup$
    – Fan Zheng
    Commented Dec 19, 2015 at 18:13
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    $\begingroup$ @FanZheng it is the functor of points approach. Grothendieck urged to abandon the previous definition in favor of this more functorial one. Some illuminating information about the petit and gros toposes can be found here. $\endgroup$
    – Arrow
    Commented Dec 19, 2015 at 18:50
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    $\begingroup$ @Arrow then I will do it on your behalf! $\endgroup$
    – David Roberts ♦
    Commented Dec 20, 2015 at 10:54
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    $\begingroup$ @Arrow, I've sent this email to the categories list. Like Tim, I would like it seen on the nLab. Given that AG's relatives have donated his Nachscrift, I don't foresee issues... $\endgroup$
    – David Roberts ♦
    Commented Dec 22, 2015 at 11:55

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