A categorical approach to topological character theory

A Categorical Approach to Picard-vessiot Theory

Picard-Vessiot rings are present in many settings like differential Galois theory, difference Galois theory and Galois theory of Artinian simple module algebras. In this article we set up an abstract framework in which we can prove theorems on existence and uniqueness of Picard-Vessiot rings, as well as on Galois groups corresponding to the Picard-Vessiot rings. As the present approach restrict...

A Categorical Approach to Probability Theory

An Algebraic Topological Approach to Privacy: Numerical and Categorical Data

In this paper, we cast the classic problem of achieving k-anonymity for a given database as a problem in algebraic topology. Using techniques from this field of mathematics, we propose a framework for k-anonymity that brings new insights and algorithms to anonymize a database. We begin by addressing the simpler case when the data lies in a metric space. This case is instrumental to introduce th...

Another Approach to Topological Descent Theory

In the category Top of topological spaces and continuous functions we prove that descent morphisms with respect to the class IE of continuous bijections are exactly the descent mor phisms providing a new characterization of the latter in terms of sub brations IE X of the basic bration given by Top X which are essentially complete lattices Also e ective descent morphisms are characterized in ter...

Geometric-topological Based Arabic Character Recognition, a New Approach

Optical Character Recognition (OCR) is a very old and of great interest in pattern recognition field. In this paper, a new algorithm based on morphological structure is proposed for Arabic character recognition. Our proposed method uses center of mass calculation. It is invariant with the size, translation and rotation of the target image. In addition, topology-based landmarks like intersection...