Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adjointness of Suspension and Shape Path Functors   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 $1\leq k \leq n-1$.

29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat