Abstract Orientable Incidence Structure and Algorithms for Finite Bounded Acyclic Categories. II. Data Structure and Fundamental Operations

TL;DR

This paper introduces a data structure for finite bounded acyclic categories, enabling efficient encoding and manipulation of abstract orientable incidence structures through a directed acyclic multigraph with weighted edges, and explores fundamental operations from multiple perspectives.

Contribution

It presents a novel data structure for finite bounded acyclic categories and analyzes its fundamental operations from geometrical, categorical, and programming viewpoints.

Findings

Data structure effectively encodes orientable incidence structures

Fundamental operations are characterized from multiple perspectives

Potential applications in algebraic and categorical computations

Abstract

A data structure for finite bounded acyclic categories has been built, which is useful to encode and manipulate abstract orientable incidence structure. It can be represented as a directed acyclic multigraph with weighted edges, where the weighs encode the algebraic structure between edges. The fundamental operations on this data structure are investigated from geometrical, categorical and programming perspectives.