
Chapter 9
Case Study of Nonsymmetric Binary
Cubic Operads
9.1 Introduction
In this chapter we choose one particular question as a model that demon-
strates how methods of this book can be used for purposes of studying operads
with the given number of generators and relations. Let us consider the gener-
ating operation alphabet X for which
X(2) = {f}, and X(k) = ∅ for k 6= 2.
We will consider quotients of the free nonsymmetric operad T (X) by several
relations of weight 3. Similarly to how operads with relations of weight 2 are
conventionally referred to as quadratic, operads with relations of weight 3
are called cubic. In a more classical language of