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For questions about simplicial sets, simplicial (co)algebras and simplicial objects in other categories; geometric realization, Dold-Kan correspondence, simplicial resolutions etc.
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The fiber of the alternating map $X^{2n}\to \mathbb{Z}[X]$
Let $X$ be a fibrant connected simplicial set. There is a simplicial map $h_n\colon X^{2n}\to \mathbb{Z}[X]$, defined on points by $(x_1, \ldots x_{2n})\mapsto \sum\limits_{i=1}^{2n}(-1)^ix_i$. Here
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