We show that every modular category is equivalent as an additive ribbon category to the category of finite-dimensional comodules of a Weak Hopf Algebra. This Weak Hopf Algebra is finite-dimensional, split cosemisimple, weakly cofactorizable, coribbon and has trivially intersecting base algebras. In order to arrive at this characterization of modular categories, we develop a generalization of Ta...

We introduce the notion of algebras graded over a small category and give a criterion for such algebras to be semi-perfect. AMS Subject Classification (2000): 18E15,16W50.

We study the trinomial arcs J(p, k, r, n) and we prove the monotonicity of this category of arcs. Mathematics Subject Classification: 26C10, 30C15, 14H45, 26A48

We study a special sort of 2-dimensional extended Topological Quantum Field Theories (TQFTs). These are defined on open-closed cobordisms by which we mean smooth compact oriented 2-manifolds with corners that have a particular global structure in order to model the smooth topology of open and closed string worldsheets. We show that the category of open-closed TQFTs is equivalent to the category...

We define an iconic image for an object category (e.g. eiffel tower) as an image with a large clearly delineated instance of the object in a characteristic aspect. We show that for a variety of objects such iconic images exist and argue that these are the images most relevant to that category. Given a large set of images noisily labeled with a common theme, say a Flickr tag, we show how to rank...