Moore hyperrectangles on a space form a strict cubical omega-category

TL;DR

This paper generalizes Moore paths to Moore hyperrectangles, creating a strict cubical omega-category with connections, addressing a question posed by Jack Morava.

Contribution

It introduces Moore hyperrectangles as a new structure to form strict cubical omega-categories, extending the concept of Moore paths.

Findings

Establishes Moore hyperrectangles as a strict cubical omega-category

Demonstrates the structure has connections but lacks cancellation of connections

Answers a specific question posed by Jack Morava

Abstract

A question of Jack Morava is answered by generalising the notion of Moore paths to that of Moore hyperrectangles, so obtaining a strict cubical omega-category. This also has the structure of connections in the sense of Brown and Higgins, but cancellation of connections does not hold.