thm__limits_of_identity_functor.tex

\documentclass{classes/tikzcd}

\begin{document}
  \begin{tikzcd}
                        & I \ar[dl, "\xi_B" swap] \ar[dr, "\xi_C"] &   \\
    B \ar[rr, "f" swap] &                                          & C
  \end{tikzcd}

  \begin{tikzcd}
      & A \ar[d, "\alpha_I"] \ar[ddl, bend right, "\alpha_B" swap] & \\
      & I \ar[dl, "\xi_B" swap]                                    & \\
    B &                                                            &
  \end{tikzcd}

  \begin{tikzcd}
      & A \ar[d, "\alpha_I"] \ar[ddl, bend right, "g" swap] & \\
      & I \ar[dl, "\id_I" swap]                             & \\
    I &                                                     &
  \end{tikzcd}

  \begin{tikzcd}
                        & A \ar[d, dashed, "\alpha_I"] \ar[ddl, bend right, "\alpha_B" swap] \ar[ddr, bend left, "\alpha_C"] &   \\
                        & I \ar[dl, "\xi_B" swap] \ar[dr, "\xi_C"]                                                           &   \\
    B \ar[rr, "f" swap] &                                                                                                    & C
  \end{tikzcd}

  \begin{tikzcd}
                        & A \ar[d, dashed, "l_A"] \ar[ddl, bend right, "\alpha_B" swap] \ar[ddr, bend left, "\alpha_C"] &   \\
                        & L \ar[dl, "\lambda_B" swap] \ar[dr, "\lambda_C"]                                              &   \\
    B \ar[rr, "f" swap] &                                                                                               & C
  \end{tikzcd}

  \begin{tikzcd}
      & L \ar[d, "l_L"] \ar[ddl, bend right, "\lambda_L" swap] & \\
      & L \ar[dl, "\lambda_L" swap]                            & \\
    L &                                                        &
  \end{tikzcd}

  \begin{tikzcd}
                        & L \ar[dl, "\id_L" swap] \ar[dr, "\lambda_C"] &   \\
    L \ar[rr, "f" swap] &                                              & C
  \end{tikzcd}
\end{document}