  We propose a new unifying framework for Thompson-like groups using a
well-known device called operads and category theory as language. We discuss
examples of operad groups which have appeared in the literature before. As a
first application, we proof a theorem which implies that planar or symmetric or
braided operads with transformations satisfying some finiteness conditions
yield operad groups of type $F_\infty$. This unifies and extends existing
proofs that certain Thompson-like groups are of type $F_\infty$.
