In this video we introduce the idea of exponential objects. We discuss many real world examples, involving ideas like movement and temperature. We discuss relationships with adjoint functors, and how exponential objects can be used to internalize ideas about arrow composition. We also discuss the category of categories. We explain how objects and arrows in a category can be referred to externally, and how such an approach can be used to understand products and exponential objects in the category of categories. Understanding exponentiation in Cat sheds a lot of light on notions like categories of functors (for example the category of graphs).
In this video we introduce the idea of exponential objects. We discuss many real world examples, involving ideas like movement and temperature. We discuss relationships with adjoint functors, and how exponential objects can be used to internalize ideas about arrow composition. We also discuss the category of categories. We explain how objects and arrows in a category can be referred to externally, and how such an approach can be used to understand products and exponential objects in the category of categories. Understanding exponentiation in Cat sheds a lot of light on notions like categories of functors (for example the category of graphs).
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