The mathematical formalism commonly used in treating nonlocal highly singular interactions is revised. The notion of support cone is introduced which replaces that of support for nonlocalizable distributions. Such support cones are proven to exist for distributions defined on the Gelfand-Shilov spaces S, where 0 < β < 1 . This result leads to a refinement of previous generalizations of the loca...

We present here a novel approach to the analysis of common knowledge based on category theory. In particular, we model global epistemic state for given set agents through hierarchy beliefs represented by presheaf construction. Then, employing properties categorical monad, prove existence state, obtained in an iterative fashion, which all acquire some underlying statement. order guarantee fixed ...

We work over an algebraically closed field k, and consider the noncommutative deformation functor DefF of a finite family F of presheaves of modules defined over a presheaf of k-algebras A on a small category c. We develop an obstruction theory for DefF , with certain global Hochschild cohomology groups as the natural cohomology. In particular, we show how to calculate the prorepresenting hull ...

The purpose is to give a simple proof that a category is equivalent to a small category if and only if both it and its presheaf category are locally small In one of his lectures University of New South Wales on Yoneda structures SW the second author conjectured that a category A is essentially small if and only if both A and the presheaf category PA are locally small The rst author was in the a...

reduction of methoxyketon 1 by nabh4 gives methoxyketol 2. allthough acetate and tosylate of this alchohol were not seprated, benzoate ester was isolated. reduction of ketol 2 by lialh4 gives alchohol 4. ketol 9 does not react with methyl magnesium iodide, but methoxyketon 1 react with both methyl magnesium iodide and phenyl magnesium iodide gives corresponding hydrocarbons. keton 13 with pheny...

respectively. We refer to one of these as the parent category, with R or C as the indexing gadget. From a categorical perspective the different kinds of parent categories have a lot in common. We could say that Mod -R is just an additive version of Ĉ . That is a bit too glib, but the analysis of the two kinds of categories is quite similar. For each parent category there is a notion of a locali...

This paper is about importing the stable homotopy theory of symmetric spectra [4] and more generally presheaves of symmetric spectra [8] into the Morel-Voevodsky stable category [9], [11], [12]. Loosely speaking, the latter is the result of formally inverting the functor X 7→ T∧X on the category of pointed simplicial presheaves on the smooth Nisnevich site of a field within the Morel-Voevodsky ...

The theory of nominal sets is a theory for names, freshness and binders. It has recently been suggested as a framework for modelling local store because it allows for a more elementary development than the traditional presheaf models. However, when modelling the important principle of relational reasoning for local store all these models use families of relations indexed by relations on store, ...

An axiomatisation of Nominal Kleene Algebra has been proposed by Gabbay and Ciancia, and then shown to be complete and decidable by Kozen et al. However, one can think of at least four different formulations for a Kleene Algebra with names: using freshness conditions or a presheaf structure (types), and with explicit permutations or not. We formally show that these variations are all equivalent...