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The authors study Weyl symmetry from a cohomological point of view in theories including gravity in order to determine 0- and 1-cocycles (Weyl invariants and Weyl anomalies). For pedagogical reasons they rederive known results in four dimensions. Then they solve the same problem in six dimensions. The relation of Weyl anomalies to cocycles of the diffeomorphisms are determined: they can be obtained from each other by subtracting a suitable counterterm from the action. Finally it is shown by an example that such a subtraction corresponds to changing the regularisation scheme.

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