Notation 9.2.8.3. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing morphisms $f: A \rightarrow B$ and $g: X \rightarrow Y$. We let ${}_{f}\operatorname{Fun}(\Delta ^3, \operatorname{\mathcal{C}})_{g}$ denote the the iterated fiber product
\[ \{ f\} \times _{ \operatorname{Fun}( \operatorname{N}_{\bullet }( \{ 0 < 1 \} ) } \operatorname{Fun}( \Delta ^3, \operatorname{\mathcal{C}}) \times _{\operatorname{Fun}_{ \operatorname{N}_{\bullet }( \{ 2 < 3 \} )}} \{ g\} , \]
whose objects can be identified with diagrams
\[ \xymatrix@R =50pt@C=50pt{ A \ar [d]^{f} \ar [r] & X \ar [d]^{g} \\ B \ar [ur] \ar [r] & Y } \]
in the $\infty $-category $\operatorname{\mathcal{C}}$.