Naturally Related Functors and Processes

This page is a sub-page of our page on Category Theory.

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Pullback of a Functor Category:
Pullback of functor category

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

Translating from annotation-i to annotation-k:
Translate between two annotations
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:
Two naturally related processes

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Numbers are naturally related to Music:
Numbers  are Naturally Related to Music

Numbers and Vectors are naturally equivalent:
Numbers and Vectors are Naturally Equivalent

Numbers and Vectors are naturally related to Music:

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