The semester is starting today, so I will have less time to work on the stacks project unfortunately. In any case, after some revisions to “Morphisms of Spaces” and adding the necessary lemmas to “Descent on Spaces”, I have now started to edit the chapter “Algebraic Stacks”. This chapter is only going to have the stuff comparing the different ways of thinking about algebraic stacks (including presentations), and some examples. My idea is that we do not use the customary abuse of language (such as a scheme is a stack) in that chapter but in the chapters following it we do. So the first chapter on algebraic stacks is awkward, and the later chapters less so. In fact, I think I won’t even mention the separation axioms in that chapter since it works better in a chapter on morphisms of algebraic stacks.

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