Related papers: Sheaf Theory through Examples (Abridged Version)

Motivated by efforts to incorporate sheaves into networking, we seek to reinterpret pathfinding algorithms in terms of cellular sheaves, using Dijkstra's algorithm as an example. We construct sheaves on a graph with distinguished source and…

We discuss the back and forth technique in the context of presheaf model theory. The essence of the back and forth technique lies in showing the relationship between various hierarchies which calibrate similarity between two models and,…

In this paper, we deal with quantum theories on presheaves and sheaves on context categories consisting of commutative von Neumann algebras of bounded operators on a Hilbert space, from two viewpoints. One is to reduce presheaf-based topos…

This note is a part of the lecture notes of a graduate student algebraic geometry seminar held at the department of mathematics in National Taiwan Normal University, 2020 Falls. It aims to introduce an example of sheaves defined on posets…

"Theory figures" are a staple of theoretical visualization research. Common shapes such as Cartesian planes and flowcharts can be used not only to explain conceptual contributions, but to think through and refine the contribution itself.…

In classification and forecasting with tabular data, one often utilizes tree-based models. Those can be competitive with deep neural networks on tabular data and, under some conditions, explainable. The explainability depends on the depth…

We generalize the notion of a small sheaf of sets over a topological space or manifold to define the notion of a small stack of groupoids over an \'etale topological or differentiable stack. We then provide a construction analogous to the…

This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.

We introduce a notion of complexity of a complex of ell-adic sheaves on a quasi-projective variety and prove that the six operations are "continuous", in the sense that the complexity of the output sheaves is bounded solely in terms of the…

This elementary survey article was prepared for a talk at the 2016 Superschool on Derived Categories and D-branes. The goal is to outline an identification of the bounded derived category of coherent sheaves on a Calabi-Yau threefold with…

This paper introduces the concept of supermanifolds, viewed as the super-analogues of classical manifolds. Instead of treating supermanifolds as sets of points, we adopt an algebraic-geometric perspective, emphasizing the algebra of…

In this paper we introduce the theory of ends and coends in the context of enriched bicategories. This will be an enriched version of the theory introduced in [Cor16], and a bicategorical version of the classical theory of enriched…

Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…

This short introductory category theory textbook is for readers with relatively little mathematical background (e.g. the first half of an undergraduate mathematics degree). At its heart is the concept of a universal property, important…

These expanded lecture notes are based on a tutorial on categorical proof theory presented at the summer school associated with the conference "Topology, Algebra, and Categories in Logic 2021-2022." The chapter delves into various…

We collect in one place a variety of known and folklore results in enriched model category theory and add a few new twists. The central theme is a general procedure for constructing a Quillen adjunction, often a Quillen equivalence, between…

Learning to transfer considers learning solutions to tasks in a such way that relevant knowledge can be transferred from known task solutions to new, related tasks. This is important for general learning, as well as for improving the…

This the first of a series of articles dealing with abstract classification theory. The apparatus to assign systems of cardinal invariants to models of a first order theory (or determine its impossibility) is developed in [Sh:a]. It is…

The Goodwin model of endogenous growth looks to study the dynamic interaction between employment rate and worker's share of national income in an economy. The model is simplistically and elegantly described by a set of differential…

We consider some generalization of the theory of quantum states, which is based on the analysis of long standing problems and unsatisfactory situation with the possible interpretations of quantum mechanics. We demonstrate that the…