Natural Transformation

This quick post assumes a basic knowledge of categories and functors, which can be gained from a previous video post.

A natural transformation is defined for two functors (F,G: X\rightarrow Y) when for each object (x \in X) there is an arrow (\psi(x): F(x) \rightarrow G(x)) in (Y), AND we have the property that (\forall f: a \rightarrow b) the equality is true: (\psi(a) \circ G(f) = F(f) \circ \psi(b)).

I assume the name “natural” refers to the consistency found in these functor interactions (actions on arrows). Dat consistency!

Written on December 20, 2013