Remark 4.6.9.7. It follows from Corollary 4.6.9.5 that the construction
\[ (X_0, X_1, \cdots , X_ n) \mapsto \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X_0, X_1, \cdots , X_ n) \]
endows the collection of objects of $\operatorname{\mathcal{C}}$ with the structure of a Segal category (see Definition 
). We will return to this point in ยง.