Degreewise cofibration in $S_nC$

Question

Given a category $C$, we have $S_nC=Fun(Ar[n],C)$ and given $A,B\in Ob(S_n(C))$, (i.e. A,B are functors from $Ar[n]$ to $C$), then what does a morphism $f:A\to B$ in $S_nC$ mean by degreewise cofibration? Does it mean $f_{ij}:A_{ij}\to B_{ij}$ is a cofibration in $C$ for any $i,j$ ?

More is there a definition for the general cases in category theory?

Answer 1

Yes, a degreewise cofibration is a natural transformation, each component of which is a cofibration.