Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897589 | Journal of Pure and Applied Algebra | 2018 | 20 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Amit Kuber, JiÅà Rosický,