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Description
  • 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 Huçek and these subcategories were fully classified. This result should be transferred (en)
  • Cˇlem projektu je studium a ź steźn  charakterizace (slabŘ) reflektivnˇch a koreflektivnˇch podkategoriˇ algebraickěch kategoriˇ. Jednou ze z kladnˇch ot zek bude struktura reflexˇ a pýedevçˇm koreflexˇ v Łpln‚ kategorii modul… a pýˇbuzněch kategoriˇch. D…le§itěm zobecnŘnˇm koreflexe je tzv. pokrytˇ vzhledem ke týˇdŘ objekt…, zaveden‚ pro modulov‚ kategorie E. Enochsem. Jˇm vysloven  hypot‚za o existenci plochěch pokryti byla ned vno dok z na Eklofem, Enochsem a Trlifajem a nez visle Bicanem a El Bashirem. Poslednˇ pýˇstup byl pýenesen El Bashirem do Grothendieckověch kategorii a vyu§it pro charakterizaci pokrěvajˇcˇch týˇd. üeçenˇ projektu by mŘlo nav zat na tyto věsledky. Dalçˇm t‚matem bude zkoum nˇ podkategoriˇ, kter‚ jsou z roveĺ reflektivnˇa koreflektivnˇ. Pýˇpad takověchto Łplněch podkategoriˇ Abelověch grup byl studov n El Bashirem, Herrlichem a Huçkem a tyto podkategorie byly ŁplnŘ pops ny. Tento popis by mŘl bět v r mci ýeçenˇ projektu pýenesen na dalçˇ kategorie.
Title
  • Reflections, coreflections and generalizations (en)
  • Reflexe, koreflexe a jejich zobecnŘnˇ
skos:notation
  • GP201/01/D047
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  • Neuvedeno. (en)
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  • Projekt byl pýedźasnŘ ukonźen na § dost ýeçitele z d…vodu odchodu ýeçitele z pracoviçtŘ. Projekt pýinesl nov‚ věsledky v oblasti pokrytˇ a obal… algebraickěch struktur, a to jednak v klasick‚m aditivnˇm kontextu, ale i pro obecn‚ variety algeber. Podan  (cs)
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