相关论文: Higher dimensional hypercategories

A concrete analysis of the general properties and numerical characteristics of different atomic and nuclear shell systems and subnuclear particles is carried out on the base of the solution scheme for an introduced in part I physical graph…

We study an issue commonly seen with graph data analysis: many real-world complex systems involving high-order interactions are best encoded by hypergraphs; however, their datasets often end up being published or studied only in the form of…

We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…

We show that in a weak globular $\omega$-category, all composition operations are equivalent and commutative for cells with sufficiently degenerate boundary, which can be considered a higher-dimensional generalisation of the Eckmann-Hilton…

Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding…

We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalizing the one introduced by…

Opetopes are algebraic descriptions of shapes corresponding to compositions in higher dimensions. As such, they offer an approach to higher-dimensional algebraic structures, and in particular, to the definition of weak $\omega$-categories,…

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

This article develops a theory of cell combinatorics and cell 2-representations for differential graded 2-categories. We introduce two types of partial preorders, called the strong and weak preorder. We then analyse and compare them. The…

This work seeks to tackle the inherent complexity of dataspaces by introducing a novel data structure that can represent datasets across multiple levels of abstraction, ranging from local to global. We propose the concept of a multilevel…

We develop the theory of strong and commutative monads in the 2-dimensional setting of bicategories. This provides a framework for the analysis of effects in many recent models which form bicategories and not categories, such as those based…

There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…

Light-cone string diagrams have been used to reproduce the orbifold Euler characteristic of moduli spaces of punctured Riemann surfaces at low genus and with few punctures. Nakamura studied the meromorphic differential introduced by…

This paper introduces the notion of weakly globular double categories, a particular class of strict double categories, as a way to model weak 2-categories; it explores its use in defining a double category of fractions, and shows that the…

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…

In this paper we redevelop the foundations of the category theory of quasi-categories (also called infinity-categories) using 2-category theory. We show that Joyal's strict 2-category of quasi-categories admits certain weak 2-limits, among…

Graphs depict pairwise relationships between objects within a system. Higher-order interactions (HOIs), which involve more than two objects simultaneously, are common in nature. Such interactions can change the stability of a complex…

This is an overview of double categories of "open systems": systems that can interact with their environment. We focus on the variable sharing paradigm, where we compose open systems by identifying variables. This paradigm is often…

We proved in a previous work that Cattani-Sassone's higher dimensional transition systems can be interpreted as a small-orthogonality class of a topological locally finitely presentable category of weak higher dimensional transition…

We investigate the structure of two-dimensional partial cubes, i.e., of isometric subgraphs of hypercubes whose vertex set defines a set family of VC-dimension at most 2. Equivalently, those are the partial cubes which are not contractible…