TITLE: sheaves and cosheaves
QUESTION [7 upvotes]: I am struggling hard to understand the pushforwards and pullbacks of cosheaves. Are they also cosheaves? And what are quasicoherent cosheaves? Is there anything like coquasicoherent cosheaves? Please tell me a good refernce on theses topics, if there is some.

REPLY [10 votes]: I've written a preprint about (what I call) contraherent cosheaves of modules over the structure sheaf of rings of a scheme -- http://arxiv.org/abs/1209.2995 .  These are a kind of dual creatures to quasi-coherent sheaves.  The preprint will be updated and expanded (eventually).