
Chapter 6
Operadic Homological Algebra and
Gröbner Bases
Many natural examples of operads are operads whose components are chain
complexes, or at least homologically graded vector spaces. In fact, there are
two conceptually important sources of examples of that sort. Some algebraic
operads, like the celebrated operad of Gerstenhaber algebras [100], are the
homology operads of some operad whose components are topological spaces
(and composition maps are continuous). Some other algebraic operads, like the
operad of L
∞
-algebras [227], or the operad of A
∞
-algebras [241], are operads
where classical identities, like the Jacobi identity, or associativity,