Related papers: Diagrams and discrete extensions for finitary 2-re…

This paper is a rather informal guide to some of the basic theory of 2-categories and bicategories, including notions of limit and colimit, 2-dimensional universal algebra, formal category theory, and nerves of bicategories. As is the way…

On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…

This paper provides an abstract definition of some kinds of logics, called diagrammatic logics, together with a definition of morphisms and of 2-morphisms between diagrammatic logics. The definition of the 2-category of diagrammatic logics…

We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…

We present a category theoretical generalization of the Goussarov theorem for finite type invariants, relating generating sets for generalized finite type theories with diagrams systems for the corresponding topological objects. We will…

We investigate a family of one dimensional maps for which the bifurcation diagram looks differently than the usual ones. We describe and exemplify various unique and interesting phenomena arising for this family of maps.

We introduce the homogeneous and piecewise multilinear extensions and the eigenvalue problem for locally Lipschitz function pairs, in order to develop a systematic framework for relating discrete and continuous min-max problems. This also…

In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…

We introduce M\"obius strip diagram algebras (and their monoid and categorical versions) as subalgebras of a partition-style diagram calculus in which strands may carry handles and M\"obius strip features. We identify the resulting diagram…

Classical diagram categories and monoids, including the Temperley--Lieb, Brauer, and partition cases, arise as special instances of the category of two dimensional cobordisms and admit additional twists that produce a large new family of…

We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but…

The article provides an introduction to infinite-dimensional differential calculus over topological fields and surveys some of its applications, notably in the areas of infinite-dimensional Lie groups and dynamical systems.

We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…

We discuss the concepts of fine and coarse moduli spaces in the context of finite dimensional algebras over algebraically closed fields. In particular, our formulation of a moduli problem and its potential strong or weak solution is adapted…

We give an explicit description of the category of central extensions of a group scheme by a sheaf of Abelian groups. Based on this, we describe a framework for computing with central extensions of finite commutative group schemes, torsors…

Order diagrams are an important tool to visualize the complex structure of ordered sets. Favorable drawings of order diagrams, i.e., easily readable for humans, are hard to come by, even for small ordered sets. Many attempts were made to…

We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions…

Cataloging planar diagrams using the depth concept is proposed.

Derivators, introduced independently by Grothendieck and Heller in the 1980s, provide a categorical framework for studying homotopy theory. They are based on the idea that, while the homotopy 1-category of a single model category or…

The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…