Okay, let's do it, Jesus! Say we have monoids \\(M\\) and \\(N\\), which we think of as categories, each with one object which I'll call \\(\star\\)... we're smart enough to keep track of when we're talking about \\(\star_M\\) and \\(\star_N\\), I hope. Let's figure out what adjoint functors

\\[ F: M \to N, \quad G: N \to M \\]

amount to!

First of all, can you (or anyone) guess what a functor \\(F: M \to N\\) amounts to in this case? It's something familiar from the study of monoids.