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Approaching the Yoneda Lemma

YOW! Lambda Jam 2019

The Yoneda lemma is not the first thing to learn in category theory, but sooner or later it appears in studying the field. Unfortunately, there is quite a gap between the intuitive idea, "tell me your friends, and I will know who you are" , and its precise formulation. This talk aims to bridge this gap by introducing algebraic results in the middle, namely Cayley's theorem for groups and its generalization to semigroups. These are elementary enough, but at the same time they exhibit the conceptual step of representability, and the idea of studying all different things in a familiar form.