A Geometry of Multimodal Systems

TL;DR

This paper explores the mathematical structure of multimodal systems using category theory, providing a geometric perspective on axioms involving necessity and possibility operators.

Contribution

It introduces a categorical framework for multimodal systems, linking axioms to geometric structures and coherence results with distributive laws.

Findings

Categorical models of multimodal systems are developed.

Connections between axioms and geometric structures are established.

Coherence results relate to distributive laws in category theory.

Abstract

Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms. Subsequently, coherence results are proved pointing the connections with (usual and mixed) Distributive Laws. This is given as a geometrical description of certain axioms inside various systems with a number of necessity and possibility operators.