2010/12/06 by Eric R. Antokoletz, Antokoletz, Eric R.
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR
paper · pdf · doi:10.48550/arxiv.1012.1340
arxiv created 2010/12/06 · openalex publication_date 2010/12/06 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce an external version of the internal r-fold semidirect product of groups (SDP) of Carrasco and Cegarra. Just as for the classical external SDP, certain algebraic data are required to guarantee associativity of the construction. We give an algorithmic procedure for computing axioms characterizing these data. Additionally, we give criteria for determining when a family of homomorphisms from the factors of an SDP into a monoid or group assemble into a homomorphism on the entire SDP. These tools will be used elsewhere to give explicit algebraic axioms for hypercrossed complexes, which are algebraic models for classical homotopy types introduced by Carrasco and Cegarra.