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Cartesian closed stable categories q
, 2004
"... The aim of this paper is to establish some Cartesian closed categories which are between the two Cartesian closed categories: SLP (the category of Ldomains and stable functions) and DI (the full subcategory of SLP whose objects are all dIdomains). First we show that the exponentials of every full ..."
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subcategory of SLP are exactly the spaces of stable functions. Then we prove that the full subcategories SDMBC, SDCBC and SDABC of SLP which contain DI are all Cartesian closed, where the objects of SDMBC (resp., SDCBC, SDABC) are all distributive bcdomains which are meetcontinuous (resp., continuous
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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Cited by 16 (0 self)
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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
Thick subcategories of the . . .
"... We classify thick subcategories of the bounded derived category of an abelian category A in terms of subcategories of A. The proof can be applied to characterize the localizing subcategories of the full derived category of A. As an application we prove an algebraic analogon of the telescope conject ..."
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We classify thick subcategories of the bounded derived category of an abelian category A in terms of subcategories of A. The proof can be applied to characterize the localizing subcategories of the full derived category of A. As an application we prove an algebraic analogon of the telescope
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
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.
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
Refining thick subcategory theorems
 Fundamenta Mathematicae
"... Abstract. We use a Ktheory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories of rings and the stable homotopy category of spectr ..."
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Abstract. We use a Ktheory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories of rings and the stable homotopy category
Remarks on equivalences of additive subcategories
"... We study category equivalences between some additive subcategories of module categories. As its application, we show that the group of autofunctors of the category of reflexive modules over a normal domain is isomorphic to the divisor class group. 1 A necessary condition for equivalences of additiv ..."
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of additive subcategories Let R be a commutative ring. We denote the category of all finitely generated Rmodules by Rmod, and the full subcategory of Rmod consisting of all reflexive modules by ref(R). If R is a CohenMacaulay local ring, we denote the category of maximal CohenMacaulay modules by CM
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