Trivial algebras

Example 14.2.11 (Trivial algebras). Let \(D\) be an \(\infty \)-category. Applying Lemma 14.1.20 to the multimorphism operad \(\Mm _C\), we see that algebras over the trivial operad \(\Triv _D\) correspond to functors \(D \to C\): \[ \Alg _{\Triv _D}(C) \iso \Fun (D,C). \] In particular, taking \(D = *\) shows that a \(\Triv \)-algebra is simply an object of \(C\): \[ \Alg _{\Triv }(C) \iso C. \] Taking \(D = \emptyset \) shows that the \(\infty \)-category of \(\Triv _{\emptyset }\)-algebras is terminal.