Non-locality and contextuality are among the most counterintuitive aspects of quantum theory. They are difficult to study using classical logic and probability theory. In this paper we start with an effect 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 i...

Examination of genome sequences for stretches of Polypeptides corresponding to hydrophobic transmembrane a-helices, such as residues 69–101 of glycophrin A, are notoriously difficult to prepare in quantities ufficient for biophysical experiments. Simple synthetic nd purification approaches reported here have been eveloped by combining a few modifications to standard rocedures, without resorting...

This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal languag...

Abstract In times of ‘grand challenges’, design theorists dealing with complex systems are facing a dilemma: grand challenges require rule breaking, but they also the preservation, as much possible, existing resources, systems, know-how and societal values. Design for transition calls not ‘creative destruction’, preservation’. How do we model process that involves preservation’? Today, it is re...

Given a topological space X, thickening kernel is monoidal presheaf on $$({{\mathbb {R}}}_{\ge 0},+)$$ with values in the category of derived kernels X. A bi-thickening defined {R}}},+)$$ . To such kernel, one naturally associates an interleaving distance sheaves We prove that exists and unique as soon it interval containing 0, allowing us to construct (bi-)thickenings two different situations....

We describe the categorical semantics for a simply typed variant and simplified dependently of Cocon , contextual modal type theory where box modality mediates between weak function space that is used to represent higher-order abstract syntax (HOAS) trees strong describes (recursive) computations about them. What makes different from standard theories presence first-class contexts objects are c...

We prove that all unital separable continuous fields of C*-algebras over [0, 1] with fibers isomorphic to the Cuntz algebra On (2 ≤ n ≤ ∞) are trivial. More generally, we show that if A is a separable, unital or stable, continuous field over [0, 1] of Kirchberg C*-algebras satisfying the UCT and having finitely generated K-theory groups, then A is isomorphic to a trivial field if and only if th...

To any triangulated category with tensor product (K,⊗), we associate a topological space Spc(K,⊗), by means of thick subcategories of K, à la Hopkins-Neeman-Thomason. Moreover, to each open subset U of this space Spc(K,⊗), we associate a triangulated category K(U), producing what could be thought of as a presheaf of triangulated categories. Applying this to the derived category (K,⊗) := (D(X),⊗...

We study two different approaches to semantics for fairness within the categorical framework of presheaf models for concurrency [1, 2]. The first approach, used in e.g. dataflow models, is based on representing finite or infinite completed observations. A completed observation is the result of an infinite computation. A finite completed observation is then the result of an infinite computation ...

Let E be a cocomplete topos. We show that if the exact completion of E is a topos then every indecomposable object in E is an atom. As a corollary we characterize the locally connected Grothendieck toposes whose exact completions are toposes. This result strengthens both the Lawvere–Schanuel characterization of Boolean presheaf toposes and Hofstra’s characterization of the locally connected Gro...