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Operations in Leinster's Weak $ω$-Category Operad (1711.07958v1)
Published 21 Nov 2017 in math.CT
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.
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