Natural Transformation

µ = { µₐ : F a → G a | a ∈ 𝒞 }

A natural transformation, µ, between two functors, F,G : C → D, is a family of morphisms indexed by objects in 𝒞, such that for all morphisms f : a → b the following diagram commutes:

      µₐ
Fa --------> Ga
|            |
|Ff          |Gf
|            |
↓            ↓
Fb --------> Gb
      µᵦ

This diagram is called the naturality square. We write µ : F ⇒ G, and call µₐ the component of µ at a.