On Reflective and Coreflective Hulls
نویسندگان
چکیده
RÉSUMÉ. Cet article étudie l’enveloppe réflective engendrée par une sous-catégorie pleine d’une catégorie complète. Il s’agit de la plus petite sous-catégorie qui est pleine et réflective. Comme application nous obtenons l’enveloppe coréflective de la sous-catégorie pleine de cubes pointés dans la catégorie des espaces topologiques pointés. Par la suite nous déterminons l’enveloppe réflective de la catégorie des espaces metriques dans la catégorie des espaces uniformes, ainsi que certaines autres sous-catégories. ABSTRACT. This paper explores the reflective hull (smallest full reflective subcategory) generated by a full subcategory of a complete category. We apply this to obtain the coreflective hull of the full subcategory of pointed cubes inside the category of pointed topological spaces. We also find the reflective hull of the category of metric spaces inside the category of uniform spaces as well as certain subcategories.
منابع مشابه
UNIVERZITA KOMENSKÉHO V BRATISLAVE FAKULTA MATEMATIKY, FYZIKY A INFORMATIKY Katedra algebry, geometrie a didaktiky matematiky HEREDITY, HEREDITARY COREFLECTIVE HULLS AND OTHER PROPERTIES OF COREFLECTIVE SUBCATEGORIES OF CATEGORIES OF TOPOLOGICAL SPACES
This thesis deals mainly with hereditary coreflective subcategories of the category Top of topological spaces. After preparing the basic tools used in the rest of thesis we start by a question which coreflective subcategories of Top have the property SA = Top (i.e., every topological space can be embedded in a space from A). We characterize such classes by finding generators of the smallest cor...
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