Künzer, Matthias (Priv.-Doz. Dr.)Truong, Monika2025-07-0820251929996047http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-166540https://elib.uni-stuttgart.de/handle/11682/16654https://doi.org/10.18419/opus-16635I. A simplicial group models a pointed connected topological space up to homotopy. We may truncate a simplicial group in such a way that the homotopy groups in positions n and 0 are preserved. In this way, we obtain an [n,0]-simplicial group. This process gives a truncation functor from the category of simplicial groups to the category of [n,0]-simplicial groups. We construct the right-adjoint to this truncation functor that preserves homotopy groups, using methods from Conduché. II. A stable simplicial group, also called group spectrum or Kan spectrum, models a topological spectrum up to homotopy. We construct adjoint functors between the category of stable simplicial groups and the category of [n,-∞]-stable simplicial groups that respect homotopy groups. The category of [1,0]-stable simplicial groups is defined as a full subcategory of [1,-∞]-stable simplicial groups. We show that the category of [1,0]-stable simplicial groups is equivalent to the category of stable crossed modules in the sense of Conduché, using a construction of countably iterated semidirect products.eninfo:eu-repo/semantics/openAccess510doctoralThesis