Abstract
The classical Mac Lane-Whitehead equivalence showing that crossed modules of groups are algebraic models of connected homotopy 2-types has found a corresponding equivariant version by Moerdijk and Svensson ([22]). In this paper we show that this equivariant result has a higher-dimensional version which gives an equivalence between the homotopy category of diagrams of certain objects indexed by the orbit category of a group H and H-equivariant homotopy n-types for n≥1.
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Garzón, A.R., Miranda, J.G. Models for homotopy n-types in diagram categories. Appl Categor Struct 4, 213–225 (1996). https://doi.org/10.1007/BF00122253
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DOI: https://doi.org/10.1007/BF00122253