Naslov
Category Descriptions of the S_n- and S-equivalence

Autori
Červar, Branko ; Uglešić, Nikica

Izvornik
Mathematical communications (1331-0623) 13 (2008), 1; 1-19

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
compactum; ANR; shape; S-equivalence; S_{;;; n};;; -equivalence; category

Sažetak
By reducing the Marde\v{; ; ; s}; ; ; i\'{; ; ; c}; ; ; }; ; ; $S${; ; ; \small -equivalence to a finite case, i.e. to each \in\{; ; ; 0\}; ; ; \cup\mathbb{; ; ; N}; ; ; ${; ; ; \small\ separately, the authors recently derived the notion of $S_{; ; ; n}; ; ; ${; ; ; \small -equivalence of compacta. In this paper the additional notion of }; ; ; $S_{; ; ; n}; ; ; ^{; ; ; +}; ; ; $-equivalence is introduced such that $S_{; ; ; n}; ; ; ^{; ; ; +}; ; ; $ implies $S_{; ; ; n}; ; ; $ and $S_{; ; ; n}; ; ; $ implies $S_{; ; ; n-1}; ; ; ^{; ; ; +}; ; ; $. The implications $S_{; ; ; 1}; ; ; ^{; ; ; +}; ; ; \Rightarrow S_{; ; ; 1}; ; ; \Rightarrow S_{; ; ; 0}; ; ; ^{; ; ; +}; ; ; \Rightarrow S_{; ; ; 0}; ; ; $ as well as $Sh\Rightarrow S\Rightarrow S_{; ; ; 1}; ; ; $ are strict. Further, for every $n\in\mathbb{; ; ; N}; ; ; $, a category $\underline{; ; ; \mathcal{; ; ; A}; ; ; }; ; ; _{; ; ; n}; ; ; $ and a homotopy relation on its morphism sets are constructed such that the mentioned equivalence relations admit appropriate descriptions in the given settings. There exist functors of $\underline{; ; ; \mathcal{; ; ; A}; ; ; }; ; ; _{; ; ; n^{; ; ; \prime}; ; ; }; ; ; $ to $\underline{; ; ; \mathcal{; ; ; A}; ; ; }; ; ; _{; ; ; n}; ; ; $, $n\leq n^{; ; ; \prime}; ; ; $, keeping the objects fixed and preserving the homotopy relation. Finally, the $S$-equivalence admits a category characterization in the corresponding sequential category $\underline{; ; ; \mathcal{; ; ; A}; ; ; }; ; ; .

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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