### Cohomology

#### Posted by Urs Schreiber

I started writing an entry

Heuristic introduction to sheaves, cohomology and higher stacks

This is (supposed to be) a pedagogical motivation of the concepts sheaf, stack, $\infty$-stack and higher topos theory. It assumes only that the reader has a heuristic knowledge of topological spaces and aims to provide from that a heuristic but useful idea of the relevance of the circle of ideas of categories and sheaves, nonabelian cohomology, sheaf cohomology and a bit of higher topos theory.

t should be readable, but will eventually need more polishing. I’d be grateful if readers with very little or no knowledge about sheaves and cohomology could tell me how helpful or not they find this.

In the course of writing this exposition, I also created an entry

about the very general notion in the context of higher $(\infty,1)$-categorical topos theory.

This can also be understood as a contribution to the discussion at Cohomology and Computtion (week 26).

For some details and comments about how the very general discussion relates in particular to familiar abelian sheaf cohomology I created also

And let me recall how these $n$-Lab entries are supposed to work: if you see anything which causes you an urge to improve it, then: hit “edit entry” and do so! But if you make significant changes, please inform us by logging what you did at latest changes.

I also expanded the entry

on my personal $n$Lab web.

## Re: Cohomology

Hi Urs,

You say that you are trying to outline the category for Differential Nonabelian Cohomology (“central general abstract nonsense concepts”). By doing this, does this has already made you capable to see anything new regarding M-Theory, that is to discover anything, that no one has ever seen before? If you did, what was it? And if you didn’t, what kind of advantage does that give you?

What it seems to me it is a kind of skelleton of M-Theory. But I cannot see the essence. What is the essence?