Kerodon

Notation 8.6.3.1. Let $\operatorname{\mathcal{C}}$ be a simplicial set and let $\rho _{-}: \operatorname{\mathcal{C}}^{\operatorname{op}} \rightarrow \operatorname{Cospan}(\operatorname{\mathcal{C}})$ be the comparison map of Variant 8.1.7.14. For every cocartesian fibration $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$, we let $\operatorname{Cospan}^{\dagger }(\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}})$ denote the fiber product $\operatorname{Cospan}(\operatorname{\mathcal{E}})^{\mathrm{all},R}(\operatorname{\mathcal{E}}) \times _{\operatorname{Cospan}(\operatorname{\mathcal{C}}) } \operatorname{\mathcal{C}}^{\operatorname{op}}$, where $R$ is the collection of all $U$-cocartesian edges of $\operatorname{\mathcal{E}}$ (see Definition 8.1.6.1).