University of KashanMathematics Interdisciplinary Research2538-36396120210301Adjointness of Suspension and Shape Path Functors233311134810.22052/mir.2021.240322.1246ENTayyebeNasriDepartment of Pure Mathematics,
Faculty of Basic Sciences,
University of Bojnord, Bojnord, IranBehroozMashayekhyDepartment of Pure Mathematics,
Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad,
Iran0000-0001-5243-0641HaniehMirebrahimiDepartment of Pure Mathematics,
Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad,
Iran0000-0002-4212-9465Journal Article20201017In 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 $1leq k leq n-1$https://mir.kashanu.ac.ir/article_111348_667a50fe5ef11868ed6c038d281de25e.pdf