J 2018

Definable categories

KUBER, Amit Shekhar and Jiří ROSICKÝ

Basic information

Original name

Definable categories

Authors

KUBER, Amit Shekhar (356 India, belonging to the institution) and Jiří ROSICKÝ (203 Czech Republic, guarantor, belonging to the institution)

Edition

Journal of Pure and Applied Algebra, 2018, 0022-4049

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Impact factor

Impact factor: 0.797

RIV identification code

RIV/00216224:14310/18:00100780

Organization unit

Faculty of Science

UT WoS

000423247900002

Keywords in English

definable category; locally finitely presentable category; injectivity; regular topos
Změněno: 20/1/2021 13:07, prof. RNDr. Jiří Rosický, DrSc.

Abstract

V originále

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.

Links

GBP201/12/G028, research and development project
Name: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku
Investor: Czech Science Foundation