functor.dot

digraph G {
  rankdir=LR
  node [shape=none]
  edge []
  labelloc=t
  fontname="times-italic"
  style=dashed
  label="Arrows compose, so, in A, g composed with f produces the arrow (g. f).\nIf F is a functor from A to B, then every object and arrow in A is mapped to an object and arrow in B.\nTherefore (g. f) in A is mapped to F(g. f) in B.\nBut arrows compose in B, so Fg . Ff = F(g. f), i.e., the functor fusion law."

  subgraph cluster_abc {
    label=A
    bgcolor=pink
    a -> b [label=f]
    b -> c [label=g]
    a -> c [label="g . f"]
  }

  subgraph cluster_F {
    label=B
    bgcolor=steelblue1
    Fa -> Fb [label=Ff]
    Fb -> Fc [label=Fg]
    Fa -> Fc [label="F(g . f)"]
  }

  a -> Fa [label=F]
  b -> Fb [label=F]
  c -> Fc [label=F]
}