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The third volume of Peter Johnstone's massive compendium of topos theory, "Sketches of an Elephant", is yet to be published. The volume is supposed to discuss cohomology and mathematical universes in the context of topos theory. While we wait for the publication of this volume, are there any alternative (hopefully just as comprehensive) references for the aforementioned subjects?

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    $\begingroup$ Most of the material supposed to be in this last volume is only available in research paper at the present time. Basically one would need to give you different references for each subsection announced (and SGA4 would definitely be one of them, covering I guess some part of section $E3$) which might be a lot of work... $\endgroup$ Nov 21, 2016 at 10:42
  • $\begingroup$ At second thought, this could be interesting to do nonetheless... $\endgroup$ Nov 21, 2016 at 10:43

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As I said in the comment, this would involve a very large number of different references! (almost one by subsection...)

But to some extent, contributors to the nLab already started doing that and it is probably the best place to start if you are interested in material covered by this third volume: https://ncatlab.org/nlab/show/Elephant

On this page you have the announced table of content of Sketches of an elephant including volume 3, with most subsection references to page on the nLab covering the idea suggested by the title of the subsection. The nLab page itself will generally not contains enough information to reconstruct the content of the subsection but will surely contains references to other papers and books.

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    $\begingroup$ The nLab may be edited by anyone, so feel free to contribute. Advice is here: ncatlab.org/nlab/show/HomePage. $\endgroup$ Nov 22, 2016 at 11:46
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    $\begingroup$ @DavidCorfield : Good point ! I hope you didn't say that because you felt like my answer was diminishing the work done on the nLab, because that is really not the impression that I wanted to give ! $\endgroup$ Nov 22, 2016 at 12:12
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    $\begingroup$ Simon, not at all. I think perhaps, though, people don't realise just how much work has been done by a very small number of people. New recruits are always welcome. $\endgroup$ Nov 22, 2016 at 15:50
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Johnstone's 1977 book 'Topos Theory' is a very good source.

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