Catsters Video Question

Question

The first Catsters video on adjunctions has just finished, at this time, describing adjunctions in 2-categorical terms. Basically, the idea is to whisker the adjoint functors and the (co)unit of adjunction. But what's the "$1$" to which the diagrams are equal? Is it a natural transformation between the identity functors $1_{\mathsf C}$ and $1_{\mathsf D}$? Is it a natural isomorphism? If it's only a natural transformation, then we get that an adjunction really has a "direction", but shouldn't it be symmetrical?

Answer 1

The $1$ denotes the identity natural transformations on $F$ and $G$. It's more helpful to write the triangle identities in an arbitrary 2-category and work out the whiskerings.