Overview
Natural Transformations are mappings between functors. Given two functors, {% F %} and {% G %} between categories {% C %} and {% D %}, a natural transformation {% \alpha %} is a function that for every {% a \in Obj(C) %}, picks a morphism in {% D %}
{% \alpha_a : Fa \rightarrow Ga %}
Naturality Condition
For a mapping defined above, to be a natural transformation, it must satisfy the naturality condition, defined as
{% Gf \circ \alpha_a = \alpha_b \circ Ff %}