TY - JOUR
T1 - Operads as abstract algebras, and the Koszul property
AU - Shnider, Steve
AU - Van Osdol, Donovan H.
PY - 1999/11/10
Y1 - 1999/11/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0033544207&partnerID=8YFLogxK
U2 - 10.1016/s0022-4049(98)00121-2
DO - 10.1016/s0022-4049(98)00121-2
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AN - SCOPUS:0033544207
SN - 0022-4049
VL - 143
SP - 381
EP - 407
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 1-3
ER -