  The category of pruned trees has been defined by M. Batanin with the aim of
understanding the cell structure of certain E_n-operads in categorical terms.
The objects of this category are planar trees with n levels so that all leaves
are at the top level of the tree. The goal of this article is to prove that the
category of pruned trees is Koszul. This result gives us a minimal differential
graded model of this category, small complexes to compute Tor and Ext functors
in associated categories of diagrams, and allows us to generalize a recent
result of M. Livernet and B. Richter about the interpretation of E_n-homology
in terms of categorical Tor functors.
