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What would the minimal prerequisites be to tackle Illusie's (first) book on the cotangent complex?

I guess my goal, other than the moral and professional obligation to learn this 'classical' piece of maths, would be to understand perfect obstruction theories and how these come from 'pulling back structure from the associated derived moduli problem'.

References to where to learn such prerequisites are very much appreciated! (e.g. an introduction to topoi or simplicial sets for the algebro-geometric minded...)

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Patience, and some background on topoi (like Expose IV of SGA4). As I recall, Illusie gives the needed background on simplicial sets. You might want to skip most or all of the first chapter of Illusie's book on the first reading. –  Jonathan Wise Mar 15 '11 at 4:10

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