2018/02/04 by Nelson Martins-Ferreira, Martins-Ferreira, Nelson, Ahmet Emin Tatar +1
Mathematics · #18D05 #18D35 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1802.01204
openalex publication_date 2018/02/04 · openalex created_date 2018/02/23 · openalex updated_date 2026/07/28
In this work we study the notion of Whitehead sequence in the category of crossed modules and actions of crossed modules. As expected, Whitehead sequences in that context are the same as crossed squares. We investigate under which conditions a Whitehead sequence of crossed modules gives rise to an internal groupoid in the category of crossed modules. In other words, we explicitly investigate the so called "Smith is Huq" condition in the category of crossed modules.