We address simple voting games (SVGs) as mathematical objects in their own right, and study structures made up of these objects, rather than focusing on SVGs primarily as co-operative games. To this end it is convenient to employ the conceptual framework and language of category theory. This enables us to uncover the underlying unity of the basic operations involving SVGs. Mathematical Structur...

The extension of the knot group π1(S 3 \ K) to the category of tangles is introduced via a new category-theoretic construction. Through this presentation, a new avenue of proof for results about knot groups is opened.

On the occasion of the 25th anniversary of the Halifax category years, where I had the privilege of participating, I would like to dedicate this talk to The Internationalists. The content of the talk is meant as a contribution to the program of investigating the differential geometry of smooth etendues by category theoretic (and groupoid theoretic) means. It represents reflections based on long...

We report on our experience implementing category theory in Coq 8.5 . The repository of this development can be found at https://bitbucket.org/amintimany/ categories/. This implementation most notably makes use of features primitive projections for records and universe polymorphism that are new to Coq 8.5. The latter provides relative smallness and largeness in the development. This will be ela...

We introduce a semi-automated proof system for basic category-theoretic reasoning. It is based on a first-order sequent calculus that captures the basic properties of categories, functors and natural transformations as well as a small set of proof tactics that automate proof search in this calculus. We demonstrate our approach by automating the proof that the functor categories Fun[C × D,E] and...

A framework for formal analysis of aspect-oriented software development (AOSD) is proposed. AOSD is treated as enriching formal models of programs by traceable refinements that produce their systemic interfaces. Category-theoretic construction of architecture school is employed to formalize this approach. Aspect weaving and separation of concerns are defined as universal constructions. Aspect-o...

Let I = R be arbitrary. In [12, 11], the authors address the injectivity of h-maximal random variables under the additional assumption that t(C) ≤ e. We show that u is Euclidean, continuously separable and universally hyper-singular. The groundbreaking work of U. Suzuki on vectors was a major advance. This could shed important light on a conjecture of Jordan.

The Baire theory of category, which classifies sets into two distinct categories, is an important topic in the study of metric spaces. Many results in topology arise from category theory; in particular, the Baire categories are related to a topological property. Because the Baire Category Theorem involves nowhere dense sets in a complete metric space, this paper first develops the concepts of n...

This paper presents an introduction to category theory with an emphasis on those aspects relevant to the analysis of the model theory of linear logic. With this in mind, we focus on the basic definitions of category theory and categorical logic. An analysis of cartesian and cartesian closed categories and their relation to intuitionistic logic is followed by a consideration of symmetric monoida...