
Chapter 3
Nonsymmetric Operads
One of the main reasons to study associative algebras is the notion of a mod-
ule over an associative algebra, that is a vector space where an algebra acts
by endomorphisms. Similarly, when talking about some class of algebras, e.g.,
associative algebras, Lie algebras, Jordan algebras, etc., it is useful to con-
sider the collection of all operations with several arguments made of structure
operations on this algebra, and study algebraic structures of that collection.
This leads naturally to various notions of an operad. Sergei Merkulov [196]
came up with a beautiful analogy for that: similar to how the Cheshire Cat
from ...