Related papers: Chain Bundles and Category of Chains
Essentials of sheaves are briefly presented, followed by related comments on presheaves, bundles, manifolds and singularities, aiming to point to their differences not only in their different formal mathematical structures, but also in the…
It is interesting to know, how far we can generalize the notion of a group-valued cocycle keeping the property to determine a bundle. We find a generalization for pairs of cocycles and show how these generalized pairs of cocycles can still…
The goal of this article is to describe several presentations of the infinity category of algebras over some monad on the infinity category of chain complexes.
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
We define what is meant by a strict total order in a category having subobjects, products and fibre products. This allows us to define the notions of an ordered bundle X and an ordered G-set; when G=\pi_1(X) we relate these structures 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…
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 natural A_infinity-transformations and construct A_infinity-category of A_infinity-functors. The notion of non-strict units in an A_infinity-category is introduced. The 2-category of (unital) A_infinity-categories, (unital)…
We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.
In previous work, we introduced the notion of an impact bundle, showing how e.g., the h-index and the g-index can lead to such a bundle. Here we extend the set of impact bundles by a new impact bundle, based on the Zhang e-index. It is,…
For a collection of subcategories satisfying a fixed set of conditions, for example thick subcategories of a triangulated category, we define a topological space called classifying space of subcategories. We show that this space classifies…
We present a comprehensive classification theory for saturated Fell bundles over locally compact groups, utilizing data associated with their base group and unit fiber. This framework offers a unified approach to understanding the structure…
This article is devoted to investigations of a structure and homomorphisms of microbundles. Microbundles are generalizations of manifolds. For manifolds it was studied when their families of homomorphism can be supplied with the manifold…
This paper provides a bundle perspective to contextuality by introducing new categories of contextuality scenarios based on bundles of simplicial complexes and simplicial sets. The former approach generalizes earlier work on the…
Coloring numbers are one of the simplest combinatorial invariants of knots and links to describe. And with Joyce's introduction of quandles, we can understand them more algebraically. But can we extend these invariants to tangles -- knots…
Chain distance between points in a metric space is defined as the infimum of epsilon such that there is an epsilon-chain connecting these points. We call a mapping of a metric compact into the real line a chain development if it preserves…
In a bicategory of spans (an example of a 'generic bicategory') the factorization of a span (s,t) as the span (s,1) followed by (1,t) satisfies a simple universal property with respect to all factorizations in terms of the generic…
In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a…
In this paper, we explain how the abstract notion of a differential bundle in a tangent category provides a new way of thinking about the category of modules over a commutative ring and its opposite category. MacAdam previously showed that…
In recent years, bundle recommendation systems have gained significant attention in both academia and industry due to their ability to enhance user experience and increase sales by recommending a set of items as a bundle rather than…