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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, ...
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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. …