On pgs. 97-98 of Categories for the Working Mathematician, the author defines the notion of a Cartesian Closed Category:
The Problem: As far as I recall, the author never defines the notion of an exponential object $c^b$.
Now I'm aware of online definitions of an exponential object -- such as here -- but in this context is it actually required to have a definition of $c^b$? Or is the author just using $c^b$ as notation for the "the image of the functor specified (whatever it may be) by the right adjunction of $- \times b$ (whose counit is similarly notationally referred to as $e : c^b \times b \rightarrow c$)?