"GP201/01/D047" . "1"^^ . . "The aim of this project is to obtain a partial description of (weakly) reflective and coreflective subcategories of algebraic categories. Among the main problems is to describe the structure of reflections and, in particular, coreflections in the full category of modules and in its generalizations. The important type of a weak coreflection is, so called, cover with respect to a class of objects, which was introduced by E. Enochs. He claimed the existence of flat covers of modules. This conjecture was recently proved by Eklof, Enochs and Triifaj and independently by Bican and El Bashir. The later was used by El Bashir to characterize covering classes in Grothendieck categories. The project should follow these results. Another topic should be the studyof subcategories, which are at the same time reflective and coreflective. The case of such full subcategories in Abelian groups was treated by El Bashir, Herriich and Hu\u00E7ek and these subcategories were fully classified. This result should be transferred"@en . . "1"^^ . "0"^^ . "1"^^ . . . . . . "http://www.isvav.cz/projectDetail.do?rowId=GP201/01/D047"^^ . "C\u02C7lem projektu je studium a \u017A\u00A0ste\u017An\u00A0 charakterizace (slab\u0158) reflektivn\u02C7ch a koreflektivn\u02C7ch podkategori\u02C7 algebraick\u011Bch kategori\u02C7. Jednou ze z\u00A0kladn\u02C7ch ot\u00A0zek bude struktura reflex\u02C7 a p\u00FDedev\u00E7\u02C7m koreflex\u02C7 v \u0141pln\u201A kategorii modul\u2026 a p\u00FD\u02C7buzn\u011Bch kategori\u02C7ch. D\u2026le\u00A7it\u011Bm zobecn\u0158n\u02C7m koreflexe je tzv. pokryt\u02C7 vzhledem ke t\u00FD\u02C7d\u0158 objekt\u2026, zaveden\u201A pro modulov\u201A kategorie E. Enochsem. J\u02C7m vysloven\u00A0 hypot\u201Aza o existenci ploch\u011Bch pokryti byla ned\u00A0vno dok\u00A0z\u00A0na Eklofem, Enochsem a Trlifajem a nez\u00A0visle Bicanem a El Bashirem. Posledn\u02C7 p\u00FD\u02C7stup byl p\u00FDenesen El Bashirem do Grothendieckov\u011Bch kategorii a vyu\u00A7it pro charakterizaci pokr\u011Bvaj\u02C7c\u02C7ch t\u00FD\u02C7d. \u00FCe\u00E7en\u02C7 projektu by m\u0158lo nav\u00A0zat na tyto v\u011Bsledky. Dal\u00E7\u02C7m t\u201Amatem bude zkoum\u00A0n\u02C7 podkategori\u02C7, kter\u201A jsou z\u00A0rove\u013A reflektivn\u02C7a koreflektivn\u02C7. P\u00FD\u02C7pad takov\u011Bchto \u0141pln\u011Bch podkategori\u02C7 Abelov\u011Bch grup byl studov\u00A0n El Bashirem, Herrlichem a Hu\u00E7kem a tyto podkategorie byly \u0141pln\u0158 pops\u00A0ny. Tento popis by m\u0158l b\u011Bt v r\u00A0mci \u00FDe\u00E7en\u02C7 projektu p\u00FDenesen na dal\u00E7\u02C7 kategorie." . . "Reflections, coreflections and generalizations"@en . . . . . . "Reflexe, koreflexe a jejich zobecn\u0158n\u02C7" . . "0"^^ . "2009-06-15+02:00"^^ . "Neuvedeno."@en . . "Projekt byl p\u00FDed\u017Aasn\u0158 ukon\u017Aen na \u00A7\u00A0dost \u00FDe\u00E7itele z d\u2026vodu odchodu \u00FDe\u00E7itele z pracovi\u00E7t\u0158. Projekt p\u00FDinesl nov\u201A v\u011Bsledky v oblasti pokryt\u02C7 a obal\u2026 algebraick\u011Bch struktur, a to jednak v klasick\u201Am aditivn\u02C7m kontextu, ale i pro obecn\u201A variety algeber. Podan\u00A0"@cs . .