\(E_n\)-cohomology with coefficients as functor cohomology (Q341782)

\textit{M. Livernet} and \textit{B. Richter} [Math. Z. 269, No. 1--2, 193--219 (2011; Zbl 1235.13009)] interpreted \(E_n\)-homology of a commutative algebra with trivial coeficient as functor homology over a category of trees \(\mathrm{Epi}_n\). \textit{B. Fresse} and the author [J. Pure Appl. Algebra 220, No. 2, 683--710 (2016; Zbl 1348.57052)] computed the \(E_n\)-(co)homology of a commutative differential graded algebra with coefficients in a symmetric bimodule. In this paper, a functor homology interpretation of this (co)homology is given. This is achieved by enlarging the category of trees \(\mathrm{Epi}_n\) and using the axiomatic characterization of Ext and Tor.