drmt

Are you thinking about something like AlgebraicJulia, specifically Catlab.jl? It allows to specify Generalized Algebraic Theories and comes with a large list of standard theories. https://algebraicjulia.github.io/Catlab.jl/dev/apis/theories...

@theory Category{Ob,Hom} begin @op begin (→) := Hom (⋅) := compose end

  Ob::TYPE
  Hom(dom::Ob, codom::Ob)::TYPE

  id(A::Ob)::(A → A)
  compose(f::(A → B), g::(B → C))::(A → C) ⊣ (A::Ob, B::Ob, C::Ob)

  (f ⋅ g) ⋅ h == f ⋅ (g ⋅ h) ⊣ (A::Ob, B::Ob, C::Ob, D::Ob,
                                f::(A → B), g::(B → C), h::(C → D))
  f ⋅ id(B) == f ⊣ (A::Ob, B::Ob, f::(A → B))
  id(A) ⋅ f == f ⊣ (A::Ob, B::Ob, f::(A → B))

end