Related papers: Relational Sheaves for a Heyting Algebra

We study the \'etale sheafification of algebraic K-theory, called \'etale K-theory. Our main results show that \'etale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is defined at the level of categories.…

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…

This paper deals with sheaves of differential operators on noncommutative algebras. The sheaves are defined by quotienting a the tensor algebra of vector fields (suitably deformed by a covariant derivative) to ensure zero curvature. As an…

We present a functorial computation of the equivariant intersection cohomology of a hypertoric variety, and endow it with a natural ring structure. When the hyperplane arrangement associated with the hypertoric variety is unimodular, we…

Motivated by work of Yu.L. Shmul'yan a pre-order and an equivalence relation on the set of operator-valued Schur class functions are introduced and the behavior of Redheffer linear fractional transformations (LFTs) with respect to these…

We study linear functions on the space of $n \times n$ matrices over a field which preserve or strongly preserve each of Green's equivalence relations ($\mathcal{L}$, $\mathcal{R}$, $\mathcal{H}$ and $\mathcal{J}$) and the corresponding…

This paper is the first in a series of papers in which we define and study a category of "sheaves of $\mathcal Z$-modules on the set of alcoves" that carries important information on the category of representations of semisimple Lie…

We look at homotopy-coherent diagrams of spaces (after Segal, Leitch, Vogt, Mather, Cordier) over a Grothendieck site; we call these ``flexible presheaves''. After some preliminary materiel, we define the ``flexible sheaf'' condition. This…

A semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings. We generalize \v{C}ech cohomology theory and invertible sheaves to semiring schemes. In particular, when $X=\mathbb{P}^n_M$, a projective…

We introduce ``sheafification'' functors from categories of (lax monoidal) linear functors to categories of quasi-coherent sheaves (of algebras) of stacks. They generalize the homogeneous sheafification of graded modules for projective…

Let $\mathbb{X}$ be a weighted noncommutative regular projective curve over a field $k$. The category $\operatorname{Qcoh}\mathbb{X}$ of quasicoherent sheaves is a hereditary, locally noetherian Grothendieck category. We classify all…

A reduced divisor on a nonsingular variety defines the sheaf of logarithmic 1-forms. We introduce a certain coherent sheaf whose double dual coincides with this sheaf. It has some nice properties, for example, the residue exact sequence…

We describe a noncommutative deformation theory for presheaves and sheaves of modules that generalizes the commutative deformation theory of these global algebraic structures, and the noncommutative deformation theory of modules over…

We show that the cohomology table of any coherent sheaf on projective space is a convergent--but possibly infinite--sum of positive real multiples of the cohomology tables of what we call supernatural sheaves.

In this article, we develop an explicit categorical realization of sheafification based on colimits, products, and subobjects, emphasizing its behavior in algebraic and topological-algebraic settings. We prove that if $\mathcal{C}$ is a…

In this note we study symmetric monoidal functors from a symmetric monoidal 1-category to a cartesian symmetric monoidal $\infty$-category, which are in addition hypersheaves for a certain topology. We prove a symmetric monoidal version of…

This paper is devoted to the investigation of term-definable connexive implications in substructural logics with exchange and, on the semantical perspective, in sub-varieties of commutative residuated lattices (FLe-algebras). In particular,…

In this paper, we study the category $\mathscr{H}^{(\rho)}$ of semi-stable coherent sheaves of a fixed slope $\rho$ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We…

The study of Haeflier suggests that it is natural to regard a pseudogroup as an etale groupoid. We show that any etale groupoid corresponds to a pseudogroup sheaf, a new generalization of a pseudogroup. This correspondence is an analog of…

We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in \'etale charts these associative algebras…