Related papers: Brief Notes on Sheaves Theory

There have recently been several developments in synthetic mathematics using extensions of dependent type theory with univalence and higher inductive types: simplicial homotopy type theory, synthetic algebraic geometry and synthetic Stone…

In type theory, an oracle may be specified abstractly by a predicate whose domain is the type of queries asked of the oracle, and whose proofs are the oracle answers. Such a specification induces an oracle modality that captures a…

We give classifications of linear orbits of pairs of square matrices with non-vanishing discriminant polynomials over a field in terms of certain coherent sheaves with additional data on closed subschemes of the projective line. Our results…

This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.

These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

The paper provides a description of the sheaves of K\"ahler differentials of the arc space and jet schemes of an arbitrary scheme where these sheaves are computed directly from the sheaf of differentials of the given scheme. Several…

A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…

Inspired by the recent algebraic approach to classical field theory, we propose a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is the notion of observables over such sections, i.e.…

I consider configuration spaces for $N$-body problems, gauge theories and for GR in both geometrodynamical and Ashtekar variables forms, including minisuperspace and inhomogeneous perturbations thereabout in the former case. These examples…

This is the first in a series of three papers on Algebraic Set Theory. Its main purpose is to lay the necessary groundwork for the next two parts, one on Realisability and the other on Sheaf Models in Algebraic Set Theory.

We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…

I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.

We explicitly construct small triangulations for a number of well-known 3-dimensional manifolds and give a brief outline of some aspects of the underlying theory of 3-manifolds and its historical development.

This paper presents a model structure for natural transformations of diagrams of simplicial presheaves of a fixed shape, in which the weak equivalences are defined by analogy with pro-equivalences between pro-objects.

This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the additive canon. Of particular interest are problems about the…

Sheaves of structures are useful to give constructions in universal algebra and model theory. We can describe their logical behavior in terms of Heyting-valued structures. In this paper, we first provide a systematic treatment of sheaves of…

We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that of…

From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…

We introduce weaves, which are random sets of non-crossing c\`{a}dl\`{a}g paths that cover space-time $\overline{\mathbb{R}}\times\overline{\mathbb{R}}$. The Brownian web is one example of a weave, but a key feature of our work is that we…

We start developing a notion of reciprocity sheaves, generalizing Voevodsky's homotopy invariant presheaves with transfers which were used in the construction of his triangulated categories of motives. We hope reciprocity sheaves will…