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@article{1402351,
author = {Kuber, Amit Shekhar and Rosický, Jiří},
article_number = {5},
keywords = {definable category; locally finitely presentable category; injectivity; regular topos},
language = {eng},
issn = {0022-4049},
journal = {Journal of Pure and Applied Algebra},
title = {Definable categories},
url = {https://www.sciencedirect.com/science/article/abs/pii/S0022404917301251},
volume = {222},
year = {2018}
}
TY - JOUR
ID - 1402351
AU - Kuber, Amit Shekhar - Rosický, Jiří
PY - 2018
TI - Definable categories
JF - Journal of Pure and Applied Algebra
VL - 222
IS - 5
SP - 1006-1025
EP - 1006-1025
SN - 00224049
KW - definable category
KW - locally finitely presentable category
KW - injectivity
KW - regular topos
UR - https://www.sciencedirect.com/science/article/abs/pii/S0022404917301251
L2 - https://www.sciencedirect.com/science/article/abs/pii/S0022404917301251
N2 - 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.
ER -
KUBER, Amit Shekhar a Jiří ROSICKÝ. Definable categories. \textit{Journal of Pure and Applied Algebra}. 2018, roč.~222, č.~5, s.~1006-1025. ISSN~0022-4049.
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