ИСТИНА

Cohomology with supports in a predefined family, in addition to numerous abstract examples generalizing cohomology with compact supports, have perhaps the only concrete example in mathematics that represents nontrivial support families. Such an example gives us the Hochschild cohomology of the group algebra R[G], which are isomorphic to the classical cohomology of the classifying space BGr of the groupoid Gr associated with the attached action of the group G. These Hochschild cohomology of the group algebra R[G], is isomorphic to the classical cohomology of the classifying space BGr of the groupoid Gr, whose supports belong to specific families of supports Φn in n?dimensional skeleton (BGr)[n] of the classifying space BGr of the groupoid Gr generated by the adjoint action of the group G: