Definable categories |
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Authors: | Amit Kuber Jiří Rosický |
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Affiliation: | Department of Mathematics and Statistics, Masaryk University, Faculty of Sciences, Kotlá?ská 2, 611 37 Brno, Czech Republic |
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Abstract: | We introduce the notion of a definable category–a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are precisely the finite-injectivity classes. We prove a 2-duality between the 2-category of small exact categories and the 2-category of definable categories, and provide a new proof of its additive version. We further introduce a third vertex of the 2-category of regular toposes and show that the diagram of 2-(anti-)equivalences between three 2-categories commutes; the corresponding additive triangle is well-known. |
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Keywords: | 18C35 18E10 03G30 18C10 |
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