[OFFTOPIC] Offensive jokes

Rahim is a little Pakistani orphan who walks 5 miles to school each day. With a donation as small as 2 pennies a month, we can buy a whip and make the lazy bastard run!

homeomorphic inclusion functor left adjoint to reflective subcategory

If F and G are a pair of adjoint functors, with F left adjoint to G, then the composition G \circ F is a monad. Therefore, a monad is an endofunctor. If F and G are inverse functors the corresponding monad is the identity functor. In general adjunctions are not equivalences — they relate categories of different natures. The monad theory matters as part of the effort to capture what it is that adjunctions 'preserve'. The other half of the theory, of what can be learned likewise from consideration of F \circ G, is discussed under the dual theory of comonads.