Kerodon

Variant 7.6.2.6. Let $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. We say that a diagram $\sigma : \Delta ^1 \times \Delta ^1 \rightarrow \operatorname{\mathcal{C}}$ is a $U$-pullback square if it is a $U$-limit diagram in $\operatorname{\mathcal{C}}$ (Definition 7.1.6.1). We say that $\sigma $ is a $U$-pushout square if it is a $U$-colimit diagram in the $\infty $-category $\operatorname{\mathcal{C}}$.