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23 votes
2 answers
2k views

What is the correct definition of localisation of a category?

Disclaimer: I wasn't sure if this was an appropriate question for MathOverflow, and so I've also asked this on StackExchange. There appears to be a discrepancy in the literature regarding the ...
4 votes
1 answer
290 views

Ore localization and model structures

The question is this: Suppose C is a category, with a given multiplicatively closed set of morphisms S ⊆ C. The role of the denominator conditions on S is rather similar to the role of a Quillen ...
6 votes
1 answer
644 views

(Co)localization of the derived category

Let me start saying that a similar question can be stated for general locally Noetherian Grothendieck categories but I state it for categories of modules as it is simpler. So we fix a right Noetherian ...
3 votes
1 answer
217 views

Does Wolbert's derived equivalence between $E_*^R$-local $R$-modules and $R_E$-modules come from a Quillen equivalence?

Let $R$ be a ring spectrum (in the world of EKMM $S$-modules) and let $E$ be a smashing $R$-module. Denote by $R_E$ the $E_*$-localization of $R$. By a theorem of Wolbert (Theorem 2 in Classifying ...