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Approaching the Yoneda Lemma • Attila Egri-Nagy • YOW! 2019
Learn how the Yoneda lemma is a fundamental concept in category theory, linking monoids and semigroups, and discover how it can be approached from a group-theoretic perspective to uncover its beauty and depth.
- Groups can be represented as permutations: A group can be represented as a group of permutations, and every group is isomorphic to a permutation group.
- Cayley’s theorem: Every group is isomorphic to a permutation group, which means that a group can be represented as a set of permutations.
- Monoids and semigroups: Monoids are sets with associative binary operations, and semigroups are sets with associative binary operations that do not have to be invertible.
- Category theory: Category theory is a branch of mathematics that deals with the relationships between structures, and it provides a framework for studying monoids and semigroups.
- Symmetry: Symmetry is an important concept in mathematics that deals with the idea of preserving or leaving unchanged certain structures, and it is closely related to groups and monoids.
- Abstraction: Abstraction is a process of abstracting away from specific details to focus on general principles, and it is an important tool for studying mathematics and computer science.
- Composition: Composition is the process of combining functions or transformations to create a new one, and it is an important concept in mathematics and computer science.
- Invoking intuition: Invoking intuition involves using personal experience and understanding to make sense of mathematical concepts, and it is an important way to learn and apply mathematics.
- Practice: Practice is an important way to learn and improve skills, and it involves working with mathematical concepts and ideas in a practical setting.
- Education: Education is the process of learning and improving skills and knowledge, and it is an important part of personal and professional development.