This paper starts with an effect algebraic approach to the study of non-locality and contextuality.
Non-locality and contextuality are among the most counter- intuitive aspects of quantum theory. They are difficult to study using classical logic and probability theory. In this paper we start with an ef- fect algebraic approach to the study of non-locality and contextuality. We will see how different slices over the category of set valued functors on the natural numbers induce different settings in which non-locality and contextuality can be studied. This includes the Bell, Hardy and Kochen-Specker-type paradoxes. We link this to earlier sheaf theoretic approaches by defining a fully faithful embedding of the category of effect algebras in this presheaf category over the natural numbers.