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Pregled bibliografske jedinice broj: 455344

Časopis

Autori: Koceić Bilan, Nikola
Naslov: The induced homology and homotopy functors on the coarse shape category
Izvornik: Glasnik matematički (0017-095X) 45 (2010); 531-557
Vrsta rada: članak
Ključne riječi: topological space; polyhedron; inverse system; pro-category; pro^{;; ∗};; -category; expansion; shape; coarse shape; homotopy pro-group; homology pro-group; n-shape connectedness; kernel; exact sequence
Sažetak:
In this paper we consider some algebraic invariants of the coarse shape. We introduce functors pro^{; ; ∗}; ; -H_{; ; n}; ; and pro^{; ; ∗}; ; -π_{; ; n}; ; relating the (pointed) coarse shape category (Sh_{; ; ⋆}; ; ^{; ; ∗}; ; ) Sh^{; ; ∗}; ; to the category pro^{; ; ∗}; ; -Grp. The category (Sh_{; ; ⋆}; ; ^{; ; ∗}; ; ) Sh^{; ; ∗}; ; , which is recently constructed, is the supercategory of the (pointed) shape category (Sh_{; ; ⋆}; ; ) Sh^{; ; ∗}; ; , having all (pointed) topological spaces as objects. The category pro^{; ; ∗}; ; -Grp is the supercategory of the category of pro-groups pro-Grp, both having the same object class. The functors pro^{; ; ∗}; ; -H_{; ; n}; ; and pro^{; ; ∗}; ; -π_{; ; n}; ; extend standard functors pro-H_{; ; n}; ; and pro-π_{; ; n}; ; which operate on (Sh_{; ; ⋆}; ; ) Sh^{; ; ∗}; ; . The full analogue of the well known Hurewicz theorem holds also in Sh_{; ; ⋆}; ; ^{; ; ∗}; ; . We proved that the pro-homology (homotopy) sequence of every pair (X, A) of topological spaces, where A is normally embedded in X, is also exact in pro^{; ; ∗}; ; -Grp. Regarding this matter the following general result is obtained: for every category C with zero-objects and kernels, the category pro-C is also a category with zero-objects and kernels, while morphisms of pro^{; ; ∗}; ; -C generally don't have kernels.
Projekt / tema: 177-0372791-0886
Izvorni jezik: ENG
Rad je indeksiran u
bazama podataka:
Scopus
SCI-EXP, SSCI i/ili A&HCI
Science Citation Index Expanded (SCI-EXP) (sastavni dio Web of Science Core Collectiona)
Kategorija: Znanstveni
Znanstvena područja:
Matematika
URL cjelovitog teksta:
Časopis izlazi u samo elektroničkom izdanju: NE
Google Scholar: The induced homology and homotopy functors on the coarse shape category
Upisao u CROSBI: koceic@pmfst.hr (koceic@pmfst.hr), 29. Ožu. 2010. u 21:27 sati



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