Welcome to our third and final installment on the Yoneda lemma! In the past couple of weeks, we've slowly unraveled the mathematics behind the Yoneda perspective, i.e. the categorical maxim that an object  is completely determined by its relationships to other objects. Last week we divided this maxim into two points...

Last week we began a discussion about the Yoneda lemma. Though rather than stating the lemma (sans motivation), we took a leisurely stroll through an implication of its corollaries - the Yoneda perspective, as we called it:

 An object is completely determined by its relationships to other objects,

i.e.

by what the object "looks like" from the vantage point of each object in the category.

 But this left us wondering, What are the mathematics behind this idea? And what are the actual corollaries? In this post, we'll work to discover the answers.