Corollary 17.4.10. The colored operads \(\Assoc \), \(\oLMod \), and \(\oMod \) of Section 12.2, as well as the bimodule operad \(\oBMod \) of Definition 19.2.1, canonically define \(\infty \)-operads. Their multimorphism animae are the discrete animae associated with their classical multimorphism sets.
Proof. Apply Proposition 17.4.9 to each of the indicated colored operads. The comparison with the span model is induced by restriction along \(\Fin _* \hookrightarrow \Span (\Fin )\) and therefore preserves the fibers of hom animae over active maps. The displayed formula in the proof of Proposition 17.4.9 consequently identifies the resulting multimorphism animae with the discrete animae associated with the classical multimorphism sets. □
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