Abstract
We introduce one-sided thick subcategories \({\mathcal{C}}\) of an arbitrary preadditive category \({\mathcal{A}}\) and define a quotient category \({\mathcal{A}}/ {\mathcal{C}}\) . When \({\mathcal{A}}\) is abelian, this concept specializes to Grothendieck’s quotient for two-sided thick \({\mathcal{C}}\) . We determine the left noetherian rings for which the injective modules form a left thick subcategory. We exhibit a class of one-sided thick subcategories in categories of coherent functors which are ubiquitous in representation theory.
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