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The category of pruned trees has been defined by M. Batanin with the aim ofunderstanding 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 leavesare at the top level of the tree. The goal of this article is to prove that thecategory of pruned trees is Koszul. This result gives us a minimal differentialgraded model of this category, small complexes to compute Tor and Ext functorsin associated categories of diagrams, and allows us to generalize a recentresult of M. Livernet and B. Richter about the interpretation of E_n-homologyin terms of categorical Tor functors.

Batanin's category of pruned trees is Koszul