Brushstrokes and Tensor Products: Painting with a Monoidal Category

TL;DR

This paper introduces monoidal categories using painting analogies to make abstract mathematical concepts accessible to undergraduates and non-specialists, emphasizing visual and tactile understanding of tensor products and related structures.

Contribution

It provides an intuitive, visual approach to teaching monoidal categories, making complex ideas more accessible to beginners and non-experts.

Findings

Visual analogies clarify tensor products and associators.

Simplifies understanding of braidings and compositional tools.

Enhances pedagogical methods for category theory

Abstract

This article offers an intuitive introduction to monoidal categories through the lens of painting, presenting abstract mathematical concepts with visual and tactile analogies. Aimed at curious undergraduates and non-specialists, it seeks to demystify category theory by showing how ideas like the tensor product, associators, and braidings can be understood as compositional tools on a canvas.