Definable categories

Investor logo

Warning

This publication doesn't include Faculty of Sports Studies. It includes Faculty of Science. Official publication website can be found on muni.cz.
Authors

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

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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info