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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
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What is the core of a localization?
Let $(\mathbf{C}, \mathbf{W})$ be a relative category where $\mathbf{W}$ is saturated; i.e. it is equal to the subcategory of arrows inverted by $\gamma : \mathbf{C} \to \mathbf{C}[\mathbf{W}^{-1}]$.
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