The Clowder Project

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

1. 1.

   A natural transformation $\alpha \colon F\Longrightarrow G$.

2. 2.

   A functor $\webleft [\alpha \webright ]\colon \mathcal{C}\to \mathcal{D}^{\mathbb {1}}$ filling the diagram

   

3. 3.

   A functor $\webleft [\alpha \webright ]\colon \mathcal{C}\times \mathbb {1}\to \mathcal{D}$ filling the diagram