As I promised I would do some time ago (in a comment on Pierre-Yves Gaillard's answer), and with the hope this is useful, I have written an article in the nLab which ties together some of the results in the answers already given into a single narrative. Here and there I provide a few extra glosses and some background information.

As I promised I would do some time ago (in a comment on Pierre-Yves Gaillard's answer), and with the hope this is useful, I have written an article in the nLab which ties together some of the results in the answers already given into a single narrative. Here and there I provide a few extra glosses and some background information.