Boundary of simplex,homotopy theory

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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.