Kerodon

Remark 8.1.7.3. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the simplicial set $\operatorname{Cospan}^{\mathrm{all}, \mathrm{iso}}(\operatorname{\mathcal{C}})$ of Construction 8.1.7.2 coincides with the restricted cospan construction $\operatorname{Cospan}^{L,R}(\operatorname{\mathcal{C}})$ of Definition 8.1.6.1, where we take $L$ to be the collection of all morphisms of $\operatorname{\mathcal{C}}$ and $R$ to be the collection of all isomorphisms in $\operatorname{\mathcal{C}}$ (see Example 8.1.7.10 for a more general statement).