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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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$\mathrm{\Gamma}$ functor of Barratt-Eccles in simplicial context

In the article A free group functor for stable homotopy theory, Barratt and Eccles define for each $X\in\mathsf{sSet}_{\ast}$, the free simplicial monoid $\Gamma^{+}X$. Proposition 6.2 states i …
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