Publication details

Definable categories

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KUBER Amit Shekhar ROSICKÝ Jiří

Year of publication 2018
Type Article in Periodical
Magazine / Source Journal of Pure and Applied Algebra
MU Faculty or unit

Faculty of Science

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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