I'm looking at the book Categories of Commutative Algebras, by Yves Diers. Before plunging into the details, I'm wondering about a couple of things: (1) Does Grothendieck's theorem about faithfully flat descent work in the setting he develops? (2) What he calls algebraic spaces seem more like "bunches of varieties". The terminology "algebraic spaces" as used by Artin means something else. So does the notion of algebraic space in the sense of Artin have a place in this generalization? Allan Adler ara@altdorf.ai.mit.edu +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++