Two-dimensional regularity and exactness

BOURKE, John Denis and Richard Henry George GARNER. Two-dimensional regularity and exactness. Journal of Pure and Applied Algebra. North Holland, 2014, vol. 218, No 7, p. 1346-1371. ISSN 0022-4049. Available from: https://dx.doi.org/10.1016/j.jpaa.2013.11.021.

Basic information

• Original name: Two-dimensional regularity and exactness
• Authors: BOURKE, John Denis (372 Ireland, guarantor, belonging to the institution) and Richard Henry George GARNER (826 United Kingdom of Great Britain and Northern Ireland).
• Edition: Journal of Pure and Applied Algebra, North Holland, 2014, 0022-4049.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Netherlands
• Confidentiality degree: is not subject to a state or trade secret
• Impact factor: Impact factor: 0.474
• RIV identification code: RIV/00216224:14310/14:00073523
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1016/j.jpaa.2013.11.021
• UT WoS: 000333785200012
• Keywords in English: 2-category Exactness
• Tags: AKR, rivok

Abstract

We define notions of regularity and (Barr-)exactness for 2-categories. In fact, we define three notions of regularity and exactness, each based on one of the three canonical ways of factorising a functor in Cat: as (surjective on objects, injective on objects and fully faithful), as (bijective on objects, fully faithful), and as (bijective on objects and full, faithful). The correctness of our notions is justified using the theory of lex colimits introduced by Lack and the second author. Along the way, we develop an abstract theory of regularity and exactness relative to a kernel--quotient factorisation, extending earlier work of Street and others.

Links

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

Investor: Czech Science Foundation