A Demonstration of the Cayley Theorem for Groups - Mejía Alemán, Carlos (2021)
In this work, we will prove Cayley theorem, using category theory. We will see a different proof than the one seen in a Group Theory course, in this case we will use a famous result in category theory called the Yoneda lemma and then, to relate groups with such lemma we will take advantage of the fact that every group can be viewed as a category. This proof shows that Yoneda lemma is an extensive generalization of Cayley theorem for groups.