Let k be a field and Q a finite quiver without oriented cycles. Let kQ be the path algebra of Q and mod kQ the category of k-finite-dimensional right kQ-modules. The cluster category CQ was introduced in [1] (for general Q) and, independently, in [4] (for Q of type An). It is defined as the orbit category of the bounded derived category D(mod kQ) under the action of the automorphism Σ−1 ◦ S, wh...

We study categorical models for the unitless fragment of multiplicative linear logic. We find that the appropriate notion of model is a special kind of pro-monoidal category. Since the theory of promonoidal categories has not been developed very thoroughly, at least in the published literature, we need to develop it here. The most natural way to do this – and the simplest, once the (substantial...

a proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. a graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $g$ such that each vertex receives a color from its own list. in this paper, we prov...

We address the fact that composition in an opetopic weak n-category is in general not unique and hence is not a well-defined operation. We define composition with a given k-cell in an n-category by a span of (n− k)-categories. We characterise such a cell as universal if its composition span gives an equivalence of (n− k)-categories.

We investigate vertex operator algebras L(k, 0) associated with modular-invariant representations for an affine Lie algebra A (1) 1 , where k is ’admissible’ rational number. We show that VOA L(k, 0) is rational in the category O and find all irreducible representations in the category of weight modules.

n this paper we study the hyers-ulam-rassias stability of cauchyequation in felbin's type fuzzy normed linear spaces. as a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. this shows how the category offuzzy normed linear spaces differs from the classical normed linearspac...

The category of Yetter-Drinfeld modules YD K over a Hopf algebra K (with bijektive antipode over a field k) is a braided monoidal category. If H is a Hopf algebra in this category then the primitive elements of H do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in YD K such that the set of primitive elements P (H) is a Lie algebra in this sense...

Let M be a vector space over a field k and R ∈ End k(M ⊗ M). This paper studies what shall be called the Long equation: that is, the system of nonlinear equations R12R13 = R13R12 and R12R23 = R23R12 in End k(M ⊗ M ⊗ M). Any symmetric solution of this system supplies us a solution of the integrability condition of the Knizhnik-Zamolodchikov equation: [R12, R13+R23] = 0 ([4] or [10]). We shall ap...

Girard worked with the category of coherence spaces and continuous stable maps and observed that the functor that forgets the linearity of linear stable maps has a left adjoint. This fundamental observation gave rise to the discovery of Linear Logic. Since then, the category of coherence spaces and linear stable maps, with the comonad induced by the adjunction, has been considered a canonical m...

Predefined category exists for text categorization. In a document, text may be of any type category like government, education or health etc. many methods exist in market invented by researchers for text categorization. One of them is k-NN (k nearest neighbor) algorithm. k play a role to define number of classes for categorization. A training set is generated for each type of category to check ...