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We introduce equivariant twisted cohomology of a simplicial set equipped withsimplicial action of a discrete group and prove that for suitable twistingfunction induced from a given equivariant local coefficients, the simplicialversion of Bredon-Illman cohomology with local coefficients is isomorphic toequivariant twisted cohomology. The main aim of this paper is to prove aclassification theorem for equivariant simplicial cohomology with localcoefficients.

Equivariant Simplicial Cohomology With Local Coefficients and its Classification