2008/02/06 by Giuseppe Metere, Metere, Giuseppe
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Category Theory (math.CT) #Constraint Satisfaction and Optimization #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CT
paper · pdf · doi:10.48550/arxiv.0802.0800
PhD thesis of the author, supervisors S. Kasangian E.M. Vitale
arxiv created 2008/02/06 · openalex publication_date 2008/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Higher Dimensional Categories are showing relevant implications in several fields of mathematical research. Nevertheless basic algebraic tools, in order to further develop the theory, are far from being established. In this thesis we introduce a notion of exactness for exact sequences of pointed n-groupoids. Furthermore we test it generalizing a well known result for (fibrations of) groupoids [R.Brown, 1970]. Namely, given a fibration F of (pointed) groupoids and its strict kernel it is possible to obtain a 6-term exact sequence of groups (of loops) and pointed sets (iso classes of objects). The ziqqurath, aka step-pyramid, comes out from iterating this construction, and it consists in several sequences of n-groupoids, (n-1)-groupoids and so on up to pointed sets (0-groupoids), of increasing length.