Abstract: In this talk, I report on several works, which give insight into

the structure of Poisson cohomology, and I explain how the attempts to

generalize the definition of the Poisson complex led to the category of

Loday infinity algebras and to a graded Lie `stem’ bracket, which encodes

the cohomologies of graded Loday, Lie, Poisson, Jacobi, and Lie

infinity, as well as of 2n-ary graded Loday and Lie algebras.