Tuesday, July 13, 2010

grothendieck topology from homotopy colimits in a (2,1)-category

i don't understand much about what people are doing with various sorts of grothendieck topologies on various categories of "schemes", but i have a vague idea connected to this that i want to explore here. i want to get a grothendieck topology on the category of affine schemes (or something like that... ?perhaps just the "finitary" ones?) by embedding this category into the (2,1)-category of symmetric monoidal finitely cocomplete algebroids, and then using the homotopy colimits in this (2,1)-category to determine (in a hopefully near-obvious way) the grothendieck topology...

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