Great pictures, Michael!

Can someone explain in words the bijection between

\[ \textrm{natural transformations } \alpha: F \circ G \Rightarrow H \]

and

\[ \textrm{natural transformations } \beta: F \Rightarrow \textrm{Ran}_G(H) ? \]

Michael correctly claims there are \\(4^5\\) of each, but there is some wisdom to be gained by understanding the bijection... since this will help us with more complicated right Kan extensions.

Can someone explain in words the bijection between

\[ \textrm{natural transformations } \alpha: F \circ G \Rightarrow H \]

and

\[ \textrm{natural transformations } \beta: F \Rightarrow \textrm{Ran}_G(H) ? \]

Michael correctly claims there are \\(4^5\\) of each, but there is some wisdom to be gained by understanding the bijection... since this will help us with more complicated right Kan extensions.