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this is a message to Zoran:
I have tried to refine the section-outline at localizing subcategory a bit. Can you live with the result? Let me know.
Looks good (and I am not really expert here, though it is very relevant for what I do). Thanks for the interest in the entry. I do not see what the entry has to do with homotopy theory, though.
I do not see what the entry has to do with homotopy theory, though.
Right, as such it does not. But all the examples I can think of where people use the concept are in homotopy theory. But maybe I should remove that TOC pointer again.
Are you sure ? Maybe you mixed up localizing subcategory which is a technical name for a type of subcategories in the setting of abelian categories with “localized subcategory” or alike notion. Examples I know are used in ring theory, module theory, homological algebra…
You should list your examples in the entry. I am thinking of examples where one is interested in derived categories, such as here.
Oh, this article you point out is about localizing subcategories in the sense of triangulated categories. The current entry is not about it, namely it is about the abelian version only (apart from one reference!). One should probably split into two entries one for localizing subcategories in abelian and another for the triangulated version. I am not competent about the triangulated version, apart from basics.
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