What do we mean by equivariant chain complex? Is it a chain complex with some property ? I looked in many references and i did not find a definition of the expression "equivariant chain complex", I met this expression when reading about homology with local coefficients and it seems that they use it as a name for the cellular chain complex of the universal covering of a finite connected CW-complex $X$. It seems like it has a link with the action of $\pi_1(X)$ on the universal covering $\tilde X$ by Deck transformations but in what sense is this action equivariant ? thank you for your help !