Operads as abstract algebras, and the Koszul property

Steve Shnider, Donovan H. Van Osdol

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 characterizing 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.

Original languageEnglish
Pages (from-to)381-407
Number of pages27
JournalJournal of Pure and Applied Algebra
Issue number1-3
StatePublished - 10 Nov 1999


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