Resolutions, higher extensions and the relative Mal'tsev axiom

JOURNAL OF ALGEBRA

卷:371

Article

Everaert, Tomas^1,2  Goedecke, Julia^1,3  Van der Linden, Tim^1,4 

[1] Catholic Univ Louvain, Inst Rech Math & Phys, B-1348 Louvain, Belgium

[2] Vrije Univ Brussel, Vakgrp Wiskunde, B-1050 Brussels, Belgium

[3] Univ Cambridge, Queens Coll, Cambridge CB2 1TN, England

[4] Univ Coimbra, Ctr Matemat, P-3001454 Coimbra, Portugal

关键词: Higher extension;    Simplicial resolution;    Mal'tsev condition;    Relative homological algebra;   

DOI  :  10.1016/j.jalgebra.2012.07.036

来源: Elsevier

【 摘 要 】

We study how the concept of higher-dimensional extension which comes from categorical Galois theory relates to simplicial resolutions. For instance, an augmented simplicial object is a resolution if and only if its truncation in every dimension gives a higher extension, in which sense resolutions are infinite-dimensional extensions or higher extensions are finite-dimensional resolutions. We also relate certain stability conditions of extensions to the Kan property for simplicial objects. This gives a new proof of the fact that a regular category is Mal'tsev if and only if every simplicial object is Kan, using a relative setting of extensions. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free