Category Theory For Beginners: Universal Properties

In this video I define universal properties, universal morphisms, initial/terminal properties and initial/terminal morphisms. I illustrate how the product can be viewed as a universal morphism. I define an exponential object, and discuss how it corresponds to a universal morphism. I also define a natural number object, and describe how it corresponds to the set of natural numbers in the category of sets. I also define comma categories, and describe how universal morphisms correspond to initial/terminal objects within them. I also show that the natural number object corresponds to a universal morphism using a new proof. The proof is given in the unlisted video at https://youtu.be/h0kVqeZCdJc