lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

In [Sco] D. Scott has shown how the interpretation of intuitionistic set theory IZF in presheaf toposes can be reformulated in a more concrete fashion à la forcing as known to set theorists. In this note we show how this can be adapted to the more general case of Grothendieck toposes dealt with abstractly in [Fou, Hay].

We introduce a notion of complexity complex ℓ \ell -adic sheaves on quasi-projective variety and prove that the six operation...

In this section we will define the sheaf of relative differential forms of one scheme over another. In the case of a nonsingular variety over C, which is like a complex manifold, the sheaf of differential forms is essentially the same as the dual of the tangent bundle in differential geometry. However, in abstract algebraic geometry, we will define the sheaf of differentials first, by a purely ...

A certain Grothendieck topology assigned to a metric space gives rise sheaf cohomology theory which sees the coarse structure of space. Already constant coefficients produce interesting groups. In degree 0, they see number ends this paper, resolution via cochains is developed. It serves be valuable tool for computing cohomology. addition, homotopy invariance with established. This property can ...

In this paper, we prove that every Pre A∗-algebra A with 1 is isomorphic to the Pre A∗-algebra of all global sections of a sheaf of indecomposable Pre A∗-algebra over Boolean space and that sheaf of indecomposable Pre A∗-algebra with 1 over Boolean space is isomorphic to the sheaf obtained from the Pre A∗-algebra of all sections of the sheaf. Copyright c © 2011 Yang’s Scientific Research Instit...

We construct a sheaf-theoretic analogue of the wrapped Fukaya category in Lagrangian Floer theory, by localizing sheaves microsupported away from some given Λ⊂S⁎M along continuation maps constructed using Guillermou-Kashiwara-Schapira sheaf quantization. When Λ is subanalytic singular isotropic, we also comparison map to compact objects unbounded Λ, and show that it an equivalence. The last sta...

Every generalized laplacian L defined on a manifold M determines a sheaf of "L-harmonic" sections namely the sheaf of local solutions of Lu = 0. We study the converse problem: to what extent this sheaf determines the operator. Our main result states that the sheaf of L-harmonic sections determines the operator up to a conformal factor. Moreover, when the operator is a covariant laplacian and th...

In this article we give an interpretation, in terms of derived de Rham complexes, Scholze's period sheaf and Tan--Tong's crystalline sheaf.