Iterated wreath product of the simplex category and iterated loop spaces

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146106Generalising Segal's approach to 1-fold loop spaces, the homotopy theory of $n$-fold loop spaces is shown to be equivalent to the homotopy theory of reduced $Θ_n$-spaces, where $Θ_n$ is an iterated wreath product of the simplex category $Δ$. A sequence of functors from $Θ_n$ to $Γ$ allows for an alternative description of the Segal-spectrum associated to a $Γ$-space. In particular, each Eilenberg-MacLane space $K(π,n)$ has a canonical reduced $Θ_n$-set model.Algebraic TopologyCategory Theory18G30; 55P48; 18G55; 55P20Iterated wreath product of the simplex category and iterated loop spacestext