Natural (category theory) | Wikipedia audio article
Channel: Subhajit Sahu
Date: 29/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Natural_transformation


00:00:40 1 Definition
00:02:45 2 Examples
00:03:02 2.1 Opposite group
00:03:12 2.2 Abelianization
00:03:53 2.3 Determinant
00:04:26 2.4 Double dual of a vector space
00:05:05 2.5 Finite calculus
00:05:13 2.6 Tensor-hom adjunction
00:05:39 3 Unnatural isomorphism
00:05:57 3.1 Example: fundamental group of torus
00:06:15 3.2 Example: dual of a finite-dimensional vector space
00:06:28 4 Operations with natural transformations
00:07:22 5 Functor categories
00:08:19 5.1 More examples
00:08:30 6 Yoneda lemma
00:08:40 7 Historical notes
00:09:10 8 See also
00:11:26 9 Notes
00:12:39 10 References
00:15:43 11 External links
00:15:49 Example: fundamental group of torus
00:18:12 {\displaystyle
00:20:47 Example: dual of a finite-dimensional vector space
00:25:44 Operations with natural transformations
00:28:06 Functor categories
00:29:04 1G and εη
00:31:12 More examples
00:31:43 Yoneda lemma
00:32:27 Historical notes
00:33:44 See also



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SUMMARY
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In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved. Hence, a natural transformation can be considered to be a "morphism of functors". Indeed, this intuition can be formalized to define so-called functor categories. 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.