Construction of the cocartesian operad

Construction 15.2.4 (Cocartesian operad). Let \(C\) be an \(\infty \)-category. We define the \(\infty \)-category \(C^{\amalg }\) as \[ C^{\amalg } := \Span _{\ct ,\all }(\Fin (C)). \] Combining Lemma 15.2.3 with Lemma 13.3.8, we see that this is a semiadditive \(\infty \)-category, with finite products and finite coproducts both induced by the unordered concatenation of tuples in \(C\). We denote by \[ p_C^{\amalg }:= \Span (q)\colon C^{\amalg } \to \Span (\Fin ) \] the induced functor to \(\Span (\Fin )\), which preserves finite products.