The definition and basic properties of nef locally free sheaves appear for instance in the second volume of Lazarsfeld's book "Positivity in Algebraic Geometry" (beginning of chapter 6).
However, I am in a situation where some of the sheaves I deal with are not locally free, but only coherent; so I would like to know whether there is a well-behaved notion of nefness for coherent sheaves. The only mention of this that I found is at the end of section 1 of Kodaira Dimension of Subvarieties by Peternell-Schneider-Sommese, but it is just the definition with no references and no discussion of basic properties.
So my question is: is there a reference that gives an analogue of Theorem 6.2.12 in Lazarsfeld for nef coherent sheaves? (The results I'm mostly interested in are: (a) quotient of nef is nef; (b) pullback of nef is nef; and (c) extension of nef by nef is nef.)