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• CommentRowNumber1.
• CommentAuthorJan Pax
• CommentTimeOct 5th 2014
• (edited Oct 5th 2014)

Let $U,V$ be functors between categories $C$ and $X$.
Why a dinatural transformation $\{*\}\xrightarrow{\cdot \cdot}\hom_X(U-,V-)$ is a function which selects a natural transformation $U\xrightarrow{\cdot} V$ ?

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeOct 9th 2014

Essentially by definition.

Are you asking for somebody to unwind the definition a bit more?

• CommentRowNumber3.
• CommentAuthorFosco
• CommentTimeOct 10th 2014

Urs, the OP asked similar questions on math.SE, which I promptly (and hopefully properly) answered. The main problem was that he (she?) misunderstood the meaning of the construction proposed by Mac Lane. I hope now all has been clarified.

If not, dear Jan Pax, feel free to contact me! (just comment on the thread on math.SE)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeOct 11th 2014

Okay, thanks!

If there is any explanation that would usefully be added to the nLab entry dinatural transformation, please consider doing so.