Definable categories
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Pure and Applied Algebra |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.sciencedirect.com/science/article/abs/pii/S0022404917301251 |
| Field | General mathematics |
| Keywords | definable category; locally finitely presentable category; injectivity; regular topos |
| Description | 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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