Approaching the Yoneda Lemma
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.
Outline/Structure of the Talk
 Abstract groups vs. permutation groups. Where to find a set to act on?
 Stating and proving Cayley's theorem.
 Generalizing to semigroups. The need for monoids: what happens without the identity?
 From semigroups to categories. Stating the Yoneda Lemma.
Learning Outcome
 Learn/refresh abstract algebraic concepts: groups, monoids, semigroups.
 See the high level of abstraction in category theory, in comparison with more concrete mathematical structures.
Target Audience
Developers who have heard of category theory, but find it intimidating beyond its basic concepts. Anyone enjoying mathematical abstraction.
Prerequisites for Attendees
There is no prerequisite for the talk, except willingness for following mathematical narrative.
Links
Computational semigroup theory packages:
http://gappackages.github.io/sgpdec/
https://github.com/gappackages/subsemi
https://github.com/egrinagy/kigen
Tech conference talks:
ClojuTRE 2018 https://www.youtube.com/watch?v=yGHsXSgYdg
LambdaJam 2018 https://www.youtube.com/watch?v=KWjy0lHeSY8
schedule Submitted 1 year ago
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