
192 Algebraic Operads: An Algorithmic Companion
Example 6.2.2.4. The smallest binary tree for which there is no obvious
choice of levels is ; the two possible choices of levelization correspond
to the following two ways of drawing that tree:
and .
There is another important difference to have in mind. When components
of the given operad are chain complexes, it makes sense to require the differen-
tials to be compatible with the operad structure. This leads to the definition
of a differential graded operad.
Definition 6.2.2.5 (Differential graded operad). A symmetric operad P
whose components are chain complexes is called a differential graded operad
if the