Related papers: W-types in sheaves

We define the notion of sheaf in the context of doctrines. We prove the associate sheaf functor theorem. We show that grothendieck toposes and toposes obtained by the tripos to topos construction are instances of categories of sheaves for a…

We aim to use the concept of sheaf to establish a link between certain aspects of the set of positive integers numbers, a topic corresponding to the elementary mathematics, and some fundamental ideas of contemporary mathematics. We hope…

We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…

Explicit formulae for Weber-Schafheitlin's type integrals with exponent 1 are derived. The results of these integrals are distributions on R_+.

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…

In this paper we formally define the family of sequences know as "Pea Pattern". We then analyse its behaviour and conditions for fixed and periodic points. The paper ends with a list of fixed points and cycles.

We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…

This paper makes contributions to ``pure'' sheaf model theory, the part of model theory in which the models are sheaves over a complete Heyting algebra. We start by outlining the theory in a way we hope is readable for the non-specialist.…

This is the third installment in a series of papers on algebraic set theory. In it, we develop a uniform approach to sheaf models of constructive set theories based on ideas from categorical logic. The key notion is that of a "predicative…

We define a sheaf of abelian groups whose cohomology is represented by the cotangent complex. We show how obstructions to some standard deformation problems arise as the classes of torsors under and gerbes banded by this sheaf.

This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…

In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations.…

This article is devoted to the investigation of wrap groups of connected fiber bundles. CW-groups associated with wrap groups are studied.

The purpose of this note is to record a connection between sheaves on complete Boolean algebras and conditional sets. This connection yields a transfer principle for conditional set theory. On the other hand we use conditional set theory to…

We establish a Springer theory for classical symmetric pairs. We give an explicit description of character sheaves in this setting. In particular we determine the cuspidal character sheaves.

In this paper, we study properties of nodal orders defined over arbitrary base fields. In particular we give a classification of complete real nodal orders.

We obtain a complete classification of minimal simple unitary $W$-algebras.

In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.

Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…

We describe a 2-dimensional analogue of track categories, called two-track categories, and show that it can be used to model categories enriched in 2-type mapping spaces. We also define a Baues-Wirsching type cohomology theory for track…