The other day I noticed the following. Suppose you have a space `X`; say a metric space. Let C(`X`) be the completion of `X`. We have the obvious injection `X` ⇒ C(`X`) which is a continuous function. Any continuous function can be naturally lifted to a continuous function on the completed spaces so we have a function (`X` ⇒ `Y`) ⇒ (C(`X`) ⇒ C(`Y`)). Finally the completion of a completed space is the same so there is a continuous function C(C(`X`)) ⇒ C(`X`).

Everywhere I look I see monads. Or as pfloide would say, “Everywhere you look you see adjoint functors”.