A Seifert-van Kampen theorem in non-abelian algebra
type: Item
instance of: scholarly article
title: A Seifert-van Kampen theorem in non-abelian algebra
zbMATH Open document ID: 1396.18013
author: Mathieu Duckerts-Antoine
author: Tim Van der Linden
published in: Homology, Homotopy and Applications
publication date: 2018-07-19T00:00:00Z
review text: The authors prove a Seifert-van Kampen theorem for nonabelian categories. The Seifert-van Kampen theorem is well-known in algebraic topology, and it describes the fundamental group of a topological space in terms of the fundamental groups of open, path connected subspaces which cover the space. Loosely, the theorem says that the fundamental group functor sends pullbacks and pushouts of pointed topological spaces to pushouts in the category of groups. In this article, the authors' objective is to generalise the result to the more general setting of a regular epi-reflection. Given a functor \(F\) from an algebraically coherent, semi-abelian category \(\mathcal C\) with enough regular projectives, to an almost abelian category \(\mathcal X\), the authors give sufficient conditions for the fundamental group functor \(\pi_1^F\) relative to the functor \(F\) to preserve pushouts and split monomorphisms. When the category \(\mathcal X\) is abelian, the fundamental group functor \(\pi_1^F\) coincides with the classical left derived functor.
reviewed by: Nadia Mazza
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 55U40
zbMATH DE Number: 6908503
zbMATH Keywords: derived functor
zbMATH Keywords: fundamental group
zbMATH Keywords: homology coproduct theorem
zbMATH Keywords: categorical Galois theory
zbMATH Keywords: algebraically coherent semi-abelian category
MaRDI profile type: Publication
Wikidata QID: Q129885804
DOI: 10.4310/HHA.2018.V20.N2.A5
description: scientific article; zbMATH DE number 6908503