Titlebook: Categorical Structure of Closure Operators; With Applications to D. Dikranjan,W. Tholen Book 1995 Springer Science+Business Media Dordrecht

Cupping

Ghabi A. Kaspo D.D.S., D. Orth.inite-limit preserving reflector) give rise to such closure operators. A Lawvere-Tierney topology allows for an effective construction of the reflector into its Delta-subcategory, which we describe in detail.

PARA

Basic Properties of Closure Operators,e operation for the subobjects of each object of the category. The notions of closedness and denseness associated with a closure operator are discussed from a factorization point of view. This leads to a symmetric presentation of the fundamental properties of idempotency vis-a-vis weak hereditarines

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glowing

Closure Operators, Functors, Factorization Systems,re operators are equivalently described by (generalized functorial) factorization systems. The interplay between closure operators and preradicals which we have seen for .-modules in 3.4 extends to arbitrary categories; it is described by adjunctions which are (largely) compatible with the compositi

Entirety

Regular Closure Operators,haved) category .. Depending on . one defines the .-regular closure operator of . in such a way that its dense morphisms in . are exactly the epimorphisms of .. Now everything depends on being able to “compute” the .-regular closure effectively. The strong modification of a closure operator as intro

Ophthalmologist

Subcategories Defined by Closure Operators,category . defines the Delta-subcategory Δ(.) of objects with .-closed diagonal, and sub categories appearing as Delta-subcategories are in any “good” category . characterized as the strongly epireflective ones. What then is the regular closure operator induced by Δ (.)? Under quite “topological” co

indifferent

Epimorphisms and Cowellpoweredness,d has been the theme of many research papers (see the Notes at the end of this chapter). In many cases, closure operators offer themselves as a natural tool to tackle the problem. We concentrate here on results for those categories of topology and algebra where this approach proves to be successful.

hermitage

Dense Maps and Pullback Stability,k topology and is a fundamental tool in Sheaf- and Topos Theory: Lawvere-Tierney topologies are simply idempotent and weakly hereditary closure operators (with respect to the class of monomorphisms) such that dense subobjects are stable under pullback. Localizations (=reflective subcategories with f

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Book 1995 an equally rich and interesting supply of examples. We also had to restrict the themes in our theoretical exposition. In spite of the fact that closure operators generalize the uni- versal closure operations of abelian category theory and of topos- and sheaf theory, we chose to mention these aspect