ends.txt

\[
 \begin{tikzcd}
 &C
 \arrow[ld, "\pi_X"']
 \arrow[rd, "\pi_Y"]
 \\
 P \langle X X \rangle
 \arrow[dr, "{P \langle id, f \rangle}"']
 &&P \langle Y, Y \rangle
 \arrow[dl, "{P \langle f, id \rangle}"]
 \\
 & P \langle X, Y \rangle
 \end{tikzcd}
\]

\[ \pi_A \colon \left( \int_X P \langle X, X \rangle \right) \to P \langle A, A \rangle \]

\[
 \begin{tikzcd}
 &C
 \arrow[ddl, bend right, "g_X"']
 \arrow[ddr, bend left, "g_Y"]
 \arrow[d, dashed, "h"]
 \\
 & \int_X P \langle X, X \rangle
 \arrow[ld, "\pi_X"']
 \arrow[rd, "\pi_Y"]
 \\
 P \langle X X \rangle
 \arrow[dr, "{P \langle id, f \rangle}"']
 &&P \langle Y, Y \rangle
 \arrow[dl, "{P \langle f, id \rangle}"]
 \\
 & P \langle X, Y \rangle
 \end{tikzcd}
\]