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https://en.wikipedia.org/wiki/Natural_transformation
Natural transformations are, after categories and functors, one of the most fundamental notions of category theory and consequently appear in the majority of its applications. Definition. If and are functors between the categories and , then a natural transformation from to is a ...
https://www.math3ma.com/blog/what-is-a-natural-transformation
Simply put, a natural transformation is a collection of maps from one diagram to another. And these maps are special in that they commute with the arrows in the diagrams. For example, in the picture below, the black arrows below comprise a natural …
https://www.math3ma.com/blog/what-is-a-natural-transformation-2
Example #2: double dual space. This is really the archetypical example of a natural transformation. You'll recall (or let's observe) that every finite dimensional vector space V. . is given by v ∗ i (vj) = {1, if i = j; 0 if i ≠ j. v ∗ i ( v j) = { 1, if i = j; 0 if i ≠ j. is not canonical. That is, a different choice of basis yields a ...
https://bartoszmilewski.com/2015/04/07/natural-transformations/
A natural transformation sits between two categories, the ones that are connected by the functors it transforms. We can think of it as connecting these two categories. Let’s focus on two objects of Cat — categories C and D. There is a set of natural transformations that go between functors that connect C to D.
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The definition of natural transformations. An analogy with homotopy.
https://www.quora.com/Category-Theory-What-are-natural-transformations
Answer (1 of 6): I assume you've read the answer to "What is a functor in category theory?" A natural transformation is a mapping of functors. We start with two functors, F and G, going between categories C and D. A natural transformation is best explained "point-wise," that is …
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