In this paper, we introduce a subcategory $\widetilde{ Sh}_*$ of Sh$_*$ and obtain some results in this subcategory. First we show that there is a natural bijection $Sh (\Sigma (X, x), (Y,y))\cong Sh((X,x),Sh((I, \dot{ I}),(Y,y)))$, for every $(Y,y)\in \widetilde{ Sh}_*$ and $(X,x)\in Sh_*$. By this fact, we prove that for any pointed topological space $(X,x)$ in $\widetilde{ Sh}_*$, $\check{ \pi}_n^{ top}(X,x)\cong \check{ \pi}_{ n-k}^{ top}(Sh((S^k, *),(X,x)), e_x)$, for all $1\leq k \leq n-1$.
Categories: math.AT