# Naturally Related Functors and Processes

///////

Pullback of a Functor Category:

A Schema Mapping $\, F \,$ and its corresponding Pullback Functor $\, { \triangle }_F \,$:

Translating from annotation-i to annotation-k:

Notation: If the above diagram commutes (as is indicated by the # sign), the annotation-k is said to be naturally related to the annotation-i. Natural relationships are indicated by “implication arrows”, as seen in the diagram below.

Process B is naturally related to process A:

///////

Numbers are naturally related to Music:

Numbers and Vectors are naturally equivalent:

Numbers and Vectors are naturally related to Music: