In Homotopy Ttheory, the simplicial set ∂Δn is the subobject of hom(-,n)=Δn which is generated by the (n − 1)-simplices $d^i, 0 ≤ i ≤ n$,however I do not understand here what are the morphisms in Δn$_k$=hom(k,n) for k other than $n-1$.I.e. what more precisely means "generated" here.
Boundary of simplex,homotopy theory
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homotopy-theory
simplex
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0Any subset of simplicies of a simplicial set generates a simplicial set that you can think about externally: the intersection of all sub simplicial sets containing the simplicies, or internally: the set of all simplicies given by compositions of face and degeneracy maps applied to the generating set of simplicies. – 2017-01-05
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0The morphisms $k\to n$ are the (nonstrict) order preserving maps $\{0,1,\ldots, k\} \to \{0,1,\ldots, n\}$. – 2017-01-05