Operads as abstract algebras, and the Koszul property Original Research Article

The purpose of this work is to clarify some aspects of the theory of operads – especially of Koszul operads. We describe the free operad and give the categorical bar construction in terms of it. After giving a description of operads as abstract “algebras”, we give a self-contained proof of Theorem 4.1.13 of Ginzburg and Kapranov (1994). Our approach uses two spectral sequences associated to the categorical cobar complex of a Koszul operad.