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Hochschild two-cocycles play an important role in the deformation \`a laGerstenhaber of associative algebras. The aim of this paper is to introduce thecategory of Hoch-algebras whose objects are associative algebras equipped withan extra magmatic operation \succ verifying the Hochschild two-cocyclerelation:  (x \succ y)*z+ (x*y)\succ z= x\succ (y*z)+ x*(y\succ z).  The free Hoch-algebra over a K-vector space is given in terms of planarrooted trees and the triples of operads (As,Hoch, Mag^\infty) endowed with theinfinitesimal relations are shown to be good. We then obtain an equivalence ofcategories between connected infinitesimal Hoch-bialgebras andMag^\infty-algebras.

Hochschild two-cocycles and the good triple $(As,Hoch,Mag^\infty)$