Operations in Leinster's Weak $ω$-Category Operad

Abstract: Batanin defines a weak $\omega$-category as an algebra for a certain operad. Leinster refines this idea and defines the weak $\omega$-category operad as the initial object of a category of "operads with contraction". We demonstrate how a higher category structure arises from this definition by explicitly constructing various composites, associativity and coherence laws, and an Eckmann-Hilton braiding.