This paper deals with several aspects of epimorphisms in the category MFrm of metric frames and contractive homomorphisms. In particular, it is shown that (i) the epicomplete metric frames are uniquely determined by the power-set lattices of sets, (ii) episurjective is the same as Boolean, (iii) a metric frame has an epicompletion iff it is spatial, and (iv) the subcategory of epicomplete L in ...

The adjoint representation of a simple Lie algebra g admits a deformation into an irreducible representation R of the quantum group Uq(g). In this paper for a simply-laced g we realize R as the Grothendieck group of a particular abelian category C. There are exact functors from C to C which on the Grothendieck group act as the quantum group generators Eα, Fα, where α varies over simple roots. V...

‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.

BACKGROUND High-sensitivity C-reactive protein (hs-CRP) is a commonly used inflammatory marker. The association between hs-CRP and cancer is less consistent than that between hs-CRP and cardiovascular diseases. This study explored the association between hs-CRP and cancer, using a large database of Korean health examination records. METHODS A total of 80,781 Koreans who visited the health pro...

in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

In a word, sometimes. And it gets harder if the structure on L is not commutative. In this paper we consider the question of what properties are needed on the lattice L equipped with an operation * for several different kinds of categories built using Sets and L to have monoidal and monoidal closed structures. This works best for the Goguen category Set(L) in which membership, but not equality,...

Let g1 and g2 be two dg Lie algebras, then it is well-known that the L∞ morphisms from g1 to g2 are in 1 − 1 correspondence to the solutions of the Maurer-Cartan equation in some dg Lie algebra k(g1, g2). Then the gauge action by exponents of the zero degree component k(g1, g2) 0 on MC ⊂ k(g1, g2) 1 gives an explicit ”homotopy relation” between two L∞ morphisms. We prove that the quotient categ...

We consider locales B as algebras in the tensor category s` of sup-lattices. We show the equivalence between the Joyal-Tierney descent theorem for open localic surjections shB q −→ E in Galois theory and a Tannakian recognition theorem over s` for the s`-functor Rel(E) Rel(q ∗) −→ Rel(shB) ∼= (B-Mod)0 into the s`-category of discrete B-modules. Thus, a new Tannaka recognition theorem is obtaine...

In this paper, we present a new inductive learning method for multilabel text categorization. The proposed method uses a mutual information measure to select terms and constructs document descriptor vectors for each category based on these terms. These document descriptor vectors form a document descriptor matrix. It also uses the document descriptor vectors to construct a document-similarity m...