暇つぶし2chat MATH

- 暇つぶし2ch725: as well as in subsequent papers, e.g., papers on combinatorial anabelian geometry). Put another way, this difference may be understood as being analogous to the difference between Algebraic spaces (which form a 1-category) and (Deligne-Mumford) algebraic stacks (which form a 2-category). Of course, algebraic spaces and (Deligne-Mumford) algebraic stacks are closelyrelated, in the sense that both arise by considering gluing operations in the etale topology of schemes. On the other hand, the substantive difference between 1-and 2-categories gives rise to many substantive mathematical differences in various geometric arguments. In particular, this substantive difference between 1- and 2-categories is sufficiently significant as to render extremely strange and unnatural any attempt to use the same terminology for both algebraic spaces and algebraic stacks.

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