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327
Automorphism groups and Picard groups of additive full subcategories
, 2008
"... Abstract. We study category equivalences between additive full subcategories 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 g ..."
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Abstract. We study category equivalences between additive full subcategories 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
Reflective Full Subcategories of the Category of LPosets
"... This paper focuses on the relationship between Lposets and complete Llattices from the categorical view. By considering a special class of fuzzy closure operators, we prove that the category of complete Llattices is a reflective full subcategory of the category of Lposets with appropriate morph ..."
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This paper focuses on the relationship between Lposets and complete Llattices from the categorical view. By considering a special class of fuzzy closure operators, we prove that the category of complete Llattices is a reflective full subcategory of the category of Lposets with appropriate
A Quasitopos Containing CONV and MET as full subcategories
 Int. J. Math. and Math. Sci
, 1988
"... 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 ..."
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Cited by 14 (6 self)
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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.
PICARD GROUPS OF ADDITIVE FULL SUBCATEGORIES NAOYA HIRAMATSU AND YUJI YOSHINO
"... Let k be a commutative ring and let A be a commutative kalgebra. We denote by AMod the category of all Amodules and all Ahomomorphisms. Let C be an additive full subcategory of AMod. Since A is a kalgebra, every additive full subcategory C is a kcategory. A covariant functor C → C is called a ..."
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Let k be a commutative ring and let A be a commutative kalgebra. We denote by AMod the category of all Amodules and all Ahomomorphisms. Let C be an additive full subcategory of AMod. Since A is a kalgebra, every additive full subcategory C is a kcategory. A covariant functor C → C is called
Non trivial objectfixing endofunctors of full subcategories of finite sets
, 2000
"... fifl ffi "! ..."
Reflective subcategories
"... Reflective subcategories Given a full subcategory 3 of a category A, the existence of left 3approximations (or 3preenvelopes) 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 ..."
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Reflective subcategories Given a full subcategory 3 of a category A, the existence of left 3approximations (or 3preenvelopes) 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
Subcategories and products of categories
 Journal of Formalized Mathematics
, 1990
"... 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,b of ..."
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Cited by 29 (1 self)
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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
Classifying subcategories of modules
 Trans. Amer. Math. Soc
"... 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 su ..."
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Cited by 13 (0 self)
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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
Subcategories and Products of Categories
"... 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) for a ..."
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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
Adequate subcategories
 Illinois J. Math
"... variant functors from s? to sets. A typical example is the subcategory on one free algebra on n generators in a category of algebras with at most nary operations (n> 0) [2]. Roughly, a category with a small left adequate subcategory has a small theory. If a small subcategory sf of # is both left ..."
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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
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