A Demonstration of the Cayley Theorem for Groups

Authors

  • Carlos Mejía Alemán Facultad de Ingeniería , Universidad Nacional José María Arguedas. Andahuaylas, Perú.
  • Irene Edith Núñez Rodriguez Programa de Estudios Generales, Universidad de Lima. Lima, Perú.
  • Neisser Pino Romero Facultad de Ciencias y Filosofía, Universidad Peruana Cayetano Heredia. Lima, Perú.

DOI:

https://doi.org/10.17268/sel.mat.2021.01.09

Keywords:

Categories, functor, natural transformation, Yoneda’s Lemma, Cayley’s Theorem

Abstract

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.

References

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Mejía Alemán C. El lema de Yoneda y algunas de sus aplicaciones.[Tesis de licenciatura]. Lima: Repositorio de tesis digitales, Universidad Nacional Mayor de San Marcos; 2019.

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Adámek J, Herrlich H, Strecker GE. Abstract and Concrete Categories The Joy of Cats.[En linea]. Bremen, KatMAT Seminar; 2004. [accesado dic. 2021] Disponible en http://katmat.math.uni-bremen.de/acc/acc.pdf

Published

2021-07-29

How to Cite

Mejía Alemán, C., Núñez Rodriguez, I. E., & Pino Romero, N. (2021). A Demonstration of the Cayley Theorem for Groups. Selecciones Matemáticas, 8(01), 93 - 99. https://doi.org/10.17268/sel.mat.2021.01.09

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