Kerodon

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9.2 Discarded Diagrams

A wasteland of forgotten commutative diagrams.

9.1
\begin{equation} \label{diagram:homotopy-pushout-square-A} \begin{gathered} \xymatrix@R =50pt@C=50pt{ A \ar [r] \ar [d] & B \ar [d] \\ C \ar [r] & D} \end{gathered}\end{equation}
9.2
\begin{equation} \label{diagram:homotopy-pullback-square-A} \begin{gathered} \xymatrix@R =50pt@C=50pt{ Y \ar [r] \ar [d] & X \ar [d] \\ T \ar [r] & S. } \end{gathered}\end{equation}
9.3
\begin{equation} \begin{gathered}\label{equation:strict-Grothendieck-construction-fibration} \xymatrix@R =50pt@C=50pt{ \Lambda ^{n}_{i} \ar [r]^-{\sigma _0} \ar@ {^{(}->}[d] & \operatorname{N}_{\bullet }^{\mathscr {F}}(\operatorname{\mathcal{C}}) \ar [d]^-{ \pi } \\ \Delta ^{n} \ar [r]^-{ \overline{\sigma }} \ar@ {-->}[ur]^{ \sigma } & \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) } \end{gathered} \end{equation}