On the Finite Presentation of Operads

Operads were introduced to describe compositional structures arising in algebraic topology. Recently, some researches were interested in using operads in applied mathematics, to model composition of structures in logic, databases, and dynamical systems. In, we focus on finite presentation of an operad and its associated algebra. More precisely, we prove the general result stating that if an operad O has a finite presentation, then the associate O-algebra has also a corresponding one. Some application in physics, especially in wiring diagrams will be discussed.