Infinitesimal cubical structure, and higher connections

TL;DR

This paper introduces a novel notion of higher connections in Synthetic Differential Geometry using cubical groupoids, leveraging infinitesimal parallelepipeda derived from the manifold's diagonal neighborhood.

Contribution

It develops a new framework for higher connections based on cubical complexes and infinitesimal structures within Synthetic Differential Geometry.

Findings

Defines higher connections with cubical groupoids

Uses infinitesimal parallelepipeda from the diagonal neighborhood

Provides a new geometric perspective in Synthetic Differential Geometry

Abstract

In the context of Synthetic Differential Geometry, we describe a notion of higher connection with values in a cubical groupoid. We do this by exploiting a certain structure of cubical complex derived from the first neighbourhood of the diagonal of a manifold. This cubical complex consists of infinitesimal parallelelpipeda.