Volume 3 of Johnstone's "Sketches of an Elephant"

Question

Recently, I read the Chapter 8 of Johnstone's "Topos theory" and got interested in the homotopy and cohomology theory of Grothendieck toposes. So I'm looking for the textbooks expanding these subjects, and it seems that it will be treated in the Volume 3 of "Sketches of an Elephant".

However, unfortunately, Volume 3 has not yet been published for 10 years. So, my question is

• Volume 3 will not be published? Did he give up writing?
• Is a part of Volume 3 available? Is there a preprint?
• Does there exist a textbook which include those subjects? (Homotopy theory of toposes, Model structures for sheaves, Torsors and non-abelian cohomology, etc..)

Answer 1

Volume 3 is still in preparation. Some sections of Part F have been completed; you can try to ask the author for a copy if you're interested. I do not know if much progress has been made on Part E, but here are some alternatives:

• The original reference for the homotopy theory of toposes is [Artin and Mazur, Étale homotopy], and some aspects are discussed in [Moerdijk, Classifying spaces and classifying topoi].
• Model structures on presheaf toposes are the subject of Cisinski's thesis, [Les préfaisceaux comme modèles des types d'homotopie].
• There doesn't seem to be a coherent reference for model structures for sheaves of simplicial sets at this time.
• The original reference for non-abelian cohomology is probably [Giraud, Cohomologie non abélienne].