Naslov
The induced homology and homotopy functors on the coarse shape category

Autori
Koceić-Bilan, Nikola

Izvornik
Glasnik matematički (0017-095X) 45 (2010), 2; 531-557

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

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*-pi(n) relating the (pointed) coarse shape category (Sh(star)*) Sh* to the category pro*- Grp. The category (Sh(star)*) Sh*, which is recently constructed, is the supercategory of the (pointed) shape category (Sh(star)) 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*-pi(n) extend standard functors pro-H-n and pro-pi(n) which operate on (Sh(star)) Sh*. The full analogue of the well known Hurewicz theorem holds also in Sh(star)*. 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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