Abstract. We study category equivalences between additive full subcate-gories of module categories over commutative rings. And we are able to define the Picard group of additive full subcategories. The aim of this paper is to study the properties of the Picard groups and show that the automorphism

This paper focuses on the relationship between L-posets and complete L-lattices from the categorical view. By considering a special class of fuzzy closure operators, we prove that the category of complete L-lattices is a reflective full subcategory of the category of L-posets with appropriate

ABSTRACT. We show that convergence spaces with continuous maps and metric spaces with contractions, can be viewed as entities of the same kind. Both can be characterized by a "limit function" % which with each filter associates a map % from the underlying set to {ne extended positive real line. Continuous maps and contractions can both be (htacterized as limit function preserving maps. lhe properties common to both the convergence and metric case serve as a basis for tne definition of the category, CAP. We show that CAP is a quasitopos and that, apart from the categories CONV, of convergence spaces, and MET, of metric spaces, it also contains the category AP of approach spaces as nicely embedded subcategorles.

Let k be a commutative ring and let A be a commutative k-algebra. We denote by A-Mod the category of all A-modules and all A-homomorphisms. Let C be an additive full subcategory of A-Mod. Since A is a k-algebra, every additive full subcategory C is a k-category. A covariant functor C → C is called

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Reflective subcategories Given a full subcategory 3 of a category A, the existence of left 3-approximations (or 3-preenvelopes) completing diagrams in a unique way is equivalent to the fact that 3 is reflective in A, in the classical terminology of category theory. In the first part of the paper we

inclusion functor is the injection (inclusion) map E ֒ → which sends each object and each arrow of a Subcategory E of a category C to itself (in C). The inclusion functor is faithful. Full subcategories of C, that is, those subcategories E of C such that HomE(a,b) = HomC(b,b) for any objects a

A basic problem in mathematics is to classify all objects one is studying up to isomorphism. A lesson this author learned from stable homotopy theory [HS] is that while this is almost always impossible, it is sometimes possible, and very useful, to classify collections of objects, or certain full

is defined. The inclusion functor is the injection (inclusion) map E ֒→ which sends each object and each arrow of a Subcategory E of a category C to itself (in C). The inclusion functor is faithful. Full subcategories of C, that is, those subcategories E of C such that HomE(a, b) = HomC(b, b

of these, f It is still unknown whether the abelian groups have a small right adequate subcategory. The main result of this paper is thatf a primitive category of algebras all of whose operations are at most unary has a small adequate subcategory. It is known [1, 4] that every full category of algebras can