Two-dimensional regularity and exactness

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F14%3A00073523" target="_blank" >RIV/00216224:14310/14:00073523 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jpaa.2013.11.021" target="_blank" >http://dx.doi.org/10.1016/j.jpaa.2013.11.021</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2013.11.021" target="_blank" >10.1016/j.jpaa.2013.11.021</a>

Result language
angličtina
Original language name
Two-dimensional regularity and exactness
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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