QUOTE wikipedia
In an abstract setting we can generally say that a projection is a mapping of a set (or of a mathematical structure) which is idempotent, which means that a projection is equal to its composition with itself. A projection may also refer to a mapping which has a left inverse. Both notions are strongly related, as follows.
Let p be an idempotent map from a set A into itself (thus p∘p = p) and B = p(A) be the image of p. If we denote by Ï€ the map p viewed as a map from A onto B and by i the injection of B into A, then we have Ï€.i= IdB. Conversely, Ï€.i = IdB implies that π∘i is…