Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661182 | Topology and its Applications | 2006 | 10 Pages |
Abstract
Let X be a k-fold homotopy coalgebra of order j with respect to the pair of adjoint functors Σk and Ωk. We show that, under some connectivity conditions on the map , Y inherits a k-fold homotopy coalgebra structure of the same order for which f is a morphism of homotopy coalgebras. In particular, this holds for skeleta of homotopy coalgebras under some mild assumptions. As a consequence, we complete results on [M. Arkowitz, M. Golasiński, Homotopy coalgebras and k-fold suspensions, Hiroshima Math. J. 27 (1997) 209–220] and [T. Ganea, Cogroups and suspensions, Invent. Math. 9 (1970) 185–197] by detecting k-fold suspensions among skeleta of k-fold homotopy coalgebras.
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