The Clowder Project

Let $F,G\colon \mathcal{C}\rightrightarrows \mathcal{D}$ be functors. The following data are equivalent:¹

1. A natural transformation $\alpha \colon F\Longrightarrow G$.
2. A functor $\webleft [\alpha \webright ]\colon \mathcal{C}\to \mathcal{D}^{\mathbb {1}}$ filling the diagram
   
3. A functor $\webleft [\alpha \webright ]\colon \mathcal{C}\times \mathbb {1}\to \mathcal{D}$ filling the diagram