Related papers: W-types in sheaves

Given a stratified topological space, we answer the question whether the functor from the derived category of constructible sheaves to the derived category of sheaves with constructible cohomology is an equivalence. We also establish basic…

In this paper, we discuss the construction of classifying spaces of fibre sequences in model categories of simplicial sheaves. One construction proceeds via Brown representability and provides a classification in the pointed model category.…

We give the description of the t-structure on the derived category of regular holonomic D-modules corresponding to the trivial t-structure on the derived category of constructible sheaves via Riemann-Hilbert correspondence. We give also the…

As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex systems where extensive structure is available, but must be drawn…

The Fourier-Mukai transform is lifted to the derived category of sheaves with connection on abelian varieties. The case of flat connections (D-modules) is discussed in detail.

We classify exterior fibrations in the exterior homotopy category. As a result we also classify proper fibrations between CW-complexes.

Weierstrass-type representations have been used extensively in surface theory to create surfaces with special curvature properties. In this paper we give a unified description of these representations in terms of classical transformation…

We compare the obstruction classes defined in arXiv:1101.4069 to those defined by Illusie. We also give sheaf theoretic proofs of some of the standard properties of the cotangent complex.

We prove that the categories of coherent sheaves over weighted projective lines of tubular type are explicitly related to each other via the equivariantization with respect to certain cyclic group actions.

These notes provide a description of the abelian categories that arise as categories of coherent sheaves on weighted projective lines. Two different approaches are presented: one is based on a list of axioms and the other yields a…

We give sufficient conditions to find all subtypes isomorphic to a subtype in a finite generalized ordered type.

We characterise and investigate co-Higgs sheaves and associated algebraic and combinatorial invariants on toric varieties. In particular, we compute explicit examples.

In this note, finite type epimorphisms of rings are characterized.

Cosheaves are a dual notion of sheaves. In this paper, we prove existence of a dual of sheafifications, called \textit{cosheafifications}, in the $\infty$-category theory. We also prove that the $\infty$-category of $\infty$-cosheaves is…

We generalise sheaf models of intuitionistic logic to univalent type theory over a small category with a Grothendieck topology. We use in a crucial way that we have constructive models of univalence, that can then be relativized to any…

We introduce Rota-Baxter categories and construct examples of such structures.

Many complicated network problems can be easily understood on small networks. Difficulties arise when small networks are combined into larger ones. Fortunately, the mathematical theory of sheaves was constructed to address just this kind of…

We introduce a class of objects which we call 'affine surfaces'. These provide families of foliations on surfaces whose dynamics we are interested in. We present and analyze a couple of examples, and we define concepts related to these in…

We show that the category of log homotopy types is a full subcategory of a category of homotopy types with modulus.

In this paper we give a complete classification of cyclically graded semisimple Lie algebras that afford cuspidal character sheaves and determine the support of the cuspidal character sheaves. This constitutes a major step towards the…