Natural Transformations and Functor Categories | Category Theory Seminar | Kinshuk Banik

This talk is a part of the ISI Students' Category Theory Seminar. CT2602: Natural Transformations and Functor Categories Speaker: Kinshuk Banik (B.Math. 2nd year) Natural transformations form the primary notion of maps between functors. We look at a bunch of motivating examples of natural transformations between some common functors. Obtaining the notion of mapping between them, we can start seeing functors as objects of some category, with morphisms being the natural transformations. This is the notion of a functor category. We end with a brief look at representable functors and natural transformations corresponding to them to make way for the Yoneda lemma. 00:34 Recap of categories and functors 06:54 Natural transformations 13:04 Example: determinants 19:10 Example: group actions 30:04 Functor categories, natural isomorphism 32:49 Example: double dual isomorphism 37:23 Representable functors 40:37 Example: power set Errata: 1. (33:52) The spaces have to be finite dimensional