Category Theory — Pullback Square

digraph pb {
  rankdir=LR;
  graph [bgcolor=transparent];
  node [shape=plain, fontname=Inter, fontsize=14];
  edge [fontname=Inter, fontsize=11];

  A [label="A"]; B [label="B"]; C [label="C"]; D [label="A ×_C B"];

  D -> A [label="p"];
  D -> B [label="q"];
  A -> C [label="f"];
  B -> C [label="g"];

  P [label="P"];
  P -> A [style=dashed];
  P -> B [style=dashed];
  P -> D [style=dashed, label="∃! u"];

  { rank=same; A B }
  { rank=same; D P }
}