Category Theory For Beginners: Duality And Functors
In this video we introduce the idea of duality, and the notion of the opposite category. We define the initial object of a category, and show that it can be viewed as the empty set, within the category of sets. We also introduce the idea of the coproduct and show that it corresponds to the discriminated union, within the category of sets. We also show how the Cartesian product can be viewed as a functor in the category of sets. More generally, we show that the categorical product can be viewed as a functor, when the categorical product of each pair of objects is defined. This also gives us a notion of the categorical product of a pair of arrows.
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