For every Grothendieck category, the subcategories closed under coproducts, subobjects, and essential extensions, as well as the cohomologically stable thick subcategories, are classified by clopen subsets of a new Boolean spectrum.
Crawley-Boevey, Infinite-dimensional modules in the representation theory of finite- dimensional algebras, in Algebras and modules, I (Trondheim, 1996) , 29–54, CMS Conf
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The Boolean spectrum of a Grothendieck category
For every Grothendieck category, the subcategories closed under coproducts, subobjects, and essential extensions, as well as the cohomologically stable thick subcategories, are classified by clopen subsets of a new Boolean spectrum.