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3

Let's try a small value of $n$ first to see how it works. The first nontrivial case is $n=2$, so take $c : [0,1]^2 \to A$ a singular $2$-cube. Its boundary is $$\partial c = \sum_{i=1}^2 \sum_{\alpha \in \{0,1\}} (-1)^{i+\alpha} c_{(i,\alpha)} = -c_{(1,0)} + c_{(1,1)} + c_{(2,0)} - c_{(2,1)}.$$ If $u : [0,1] \to A$ is a singular $1$-cube, its boundary is: ...

1

Well, first we would have to have simplicially enriched functors. But $\mathrm{sk}_n : \mathbf{sSet} \to \mathbf{sSet}$ is not simplicially enriched. Indeed, any simplicially enriched functor must preserve simplicial homotopy equivalences, but $\mathrm{sk}_n$ does not preserve simplicial homotopy equivalence. (Consider the unique morphism \$\Delta^{n+1} \to ...

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