TITLE: Why the term "monad" in homological algebra?
QUESTION [8 upvotes]: Which is the origin and the reason for the choice of the term "monad" in the sense of homological algebra?
Does this concept have any relation whatsoever to the "monads" from category theory?

REPLY [5 votes]: A projective resolution "splits" into monads in the following way. 
Each exact complex of projectives  $\dots \to P_{n+1} \to P_n \to P_{n-1} \to \dots $
is a gluing of monads $0\to Z_{n} \to P_n \to Z_{n-1} \to 0$, where $Z_{k} $
is the kernel of the map $P_{k} \to P_{k-1} $. So, a monad is an elementary piece of any projective resolution, like Leibniz's monads are the elementary pieces of more complicated entities (as far as I know).