In this fourth of our series of papers on observables we show that one can associate to each von Neumann algebra R a pair of isomorphic presheaves, the upper presheaf O Rand the lower presheaf O − R , on the category of abelian von Neumann subalgebras of R. Each A ∈ Rsa induces a global section of O R and of O − R respectively. We call them contextual observables. But we show that, in general, ...

The purpose of this text is to prove all technical aspects of our model for dependent type theory with parametric quantifiers [Nuyts, Vezzosi and Devriese, 2017]. It is well-known that any presheaf category constitutes a model of dependent type theory [Hofmann, 1997], including a hierarchy of universes if the metatheory has one [Hofmann and Streicher, 1997]. We construct our model by defining t...

We present a presheaf model for the observation of infinite as well as finite computations. We apply it to give a denotational semantics of SCCS with finite delay, in which the meanings of recursion are given by final coalgebras and meanings of finite delay by initial algebras of the process equations for delay. This can be viewed as a first step in representing fairness in presheaf semantics. ...

A relative derived category for the category of modules over a presheaf of algebras is constructed to identify the relative Yoneda and Hochschild cohomologies with its homomorphism groups. The properties of a functor between this category and the relative derived category of modules over the algebra associated to the presheaf are studied. We obtain a generalization of the Special Cohomology Com...

A key aspect in extracting quantitative information from FMI logs is to segment the FMI image to get image of layers. In this paper, an automatic method based on FCM clustering and Otsu thresholding is introduced in order to extract quantitative information from FMI images. All pixels are clustered using FCM clustering algorithm at the f irst step. The second step uses KNN for other clustering....

For a small category K enriched over a suitable monoidal category V , the free completion of K under colimits is the presheaf category [K ,V ]. If K is large, its free completion under colimits is the V -category PK of small presheaves on K , where a presheaf is small if it is a left Kan extension of some presheaf with small domain. We study the existence of limits and of monoidal closed struct...

A pre-cohesive geometric morphism p : E → S satisfies Continuity if the canonical p!(X pS)→ (p!X) is an iso for every X in E and S in S. We show that if S = Set and E is a presheaf topos then, p satisfies Continuity if and only if it is a quality type. Our proof of this characterization rests on a related result showing that Continuity and Sufficient Cohesion are incompatible for presheaf topos...