Orientals and cubes, inductively

TL;DR

This paper presents inductive constructions of orientals and cubes as iterated cones and cylinders of the terminal strict globular omega-category, offering a new perspective on their structure.

Contribution

It introduces direct inductive methods to construct orientals and cubes as iterated cones and cylinders, respectively, of a fundamental omega-category.

Findings

Provides explicit inductive constructions of orientals and cubes.

Shows these structures as iterated cones and cylinders.

Enhances understanding of globular omega-categories.

Abstract

We provide direct inductive constructions of the orientals and the cubes, exhibiting them as the iterated cones, respectively, the iterated cylinders, of the terminal strict globular omega-category.