Diagrammatic Construction of Representations of Small Quantum $\mathfrak{sl}_2$

We provide a combinatorial description of the monoidal category generated by the fundamental representation of the small quantum group of $$ \mathfrak{sl} $$ 2 at a root of unity q of odd order. Our approach is diagrammatic, and it relies on an extension of the Temperley–Lieb category specialized at δ = −q − q−1.