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A branch of algebraic topology concerning the study of cocycles and coboundaries. It is in some sense a dual theory to homology theory. This tag can be further specialized by using it in conjunction with the tags group-cohomology, etale-cohomology, sheaf-cohomology, galois-cohomology, lie-algebra-cohomology, motivic-cohomology, equivariant-cohomology, ...

13 votes

Do pretopoi have cohomology and homotopy groups?

However, this observation only rules out one particular approach to cohomology. Donu already mentioned one more in the comments and there are several others. … My current favorite to constructivize and predicativize cohomology is to use of a mix of the approaches of Emily Riehl (employing pointwise Kan extensions) and the Stacks Project. …
Ingo Blechschmidt's user avatar