Representable functors, Yoneda Lemma, and universal objects

Authors

  • Isaac Javier Díaz División Académica de Ciencias Básicas de la Universidad Juárez Autónoma de Tabasco.
  • Carlos Ariel Pompeyo Guitérrez División Académica de Ciencias Básicas de la Universidad Juárez Autónoma de Tabasco.

DOI:

https://doi.org/10.19136/jobs.a11n32.6575

Keywords:

Representable functors, Yoneda’s lemma, Category Theory, Natural Transformations

Abstract

In this work we explore the concepts of representability and universal object, as well as Yoneda’s Lemma, which belong to Category Theory. We provide several examples to illustrate the concepts. In order to do this, we consider objects coming from different mathematical fields, such as Linear Algebra, Topology, Ring Theory, among others. Besides, we provide proofs for the results.

References

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[2] B. Fantechi et al., Grothendieck’s FGA Explained. In Amer. Math. Soc., 2005

[3] R. Hartshorne, Algebraic Geometry. Springer Science & Business Media.

[4] T. Hungerford, Algebra. Springer

[5] S. Mac Lane, Categories for the working mathematician. Springer Science & Business Media, 2013.

[6] J.P. Marquis, “What is Category Theory?”. Polimetrica International Scientific Publisher Monza/Italy, 2006.

[7] J. Munkres, Topology. Prentice Hall, 2009.

[8] P. Newstead, Introduction to moduli problems and orbit spaces, 2013.

[9] J. M. Lee, Introduction to Smooth Manifolds. Springer, 20013.

[10] T. Leinster, Basic category theory. Cambridge University Press, 2014.

[11] T. Tao, “Yoneda’s lemma as an identification of form and function: the case study of polynomials,” What’s new, Aug. 25, 2023. https://terrytao.wordpress.com/2023/08/25/yonedaslemma- as-an-identification-of-form-and-function-the-case-study-of-polynomials/

[12] T. Wedhorn, Manifolds, sheaves, and cohomology. Springer Spektrum, 2016.

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Published

2025-12-12

Issue

Section

Artículo científico

How to Cite

Javier Díaz, I., & Pompeyo Guitérrez, C. A. (2025). Representable functors, Yoneda Lemma, and universal objects. JOURNAL OF BASIC SCIENCES, 11(32), 68-84. https://doi.org/10.19136/jobs.a11n32.6575