Extension of an operad structure defined on a sub-S-modules

Authors

  • Jesús Sánchez-Guevara Universidad de Costa Rica, Escuela de Matemática, Montes de Oca, Costa Rica Author

DOI:

https://doi.org/10.15517/9na6rv61

Keywords:

Operads, Colimits, Differential graded modules, Polynomial operads

Abstract

This article presents a construction in the category of symmetrical operads in differential graded modules, which takes an operad defined in a sub S -module and extends it to an operad, whose underlying S -module includes the original. We call this the polynomial operad. This construction depends on the existence of colimits on the category of operads so a detailed review of this result is included.

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References

[1] B. Fresse, Homotopy of operads & Grothendiek-Teichmüller groups. unpublished. 2016. doi: 10.1090/SURV/217.1

[2] J. L. Loday y B. Vallette, Algebraic operads. Grundlehren der mathematischen Wissenschaften. Springer, 2012. doi: 10.1007/978-3-642-30362-3

[3] S. Mac Lane, Categories for the working mathematician. 2.a ed. Springer, 1998. doi: 10.1007/978-1-4757-4721-8

[4] J. P. May, The geometry of iterated loop spaces. Lecture Notes in Mathematics. Springer-Verlag Berlin Heidelberg, 1972. doi: 10.1007/BFb0067491

[5] A. Prouté, Sur la transformation d’Eilenberg-Maclane. C. R. Acad. Sc. Paris 297(1983), 193-194. url: www. researchgate . net /publication / 266687547 Sur la transformation d’Eilenberg-Mac Lane.

[6] A. Prouté, Sur la diagonal d’Alexander-Whitney. C. R. Acad. Sc. Paris 299(1984), 391-392. url: www.researchgate.net/publication/267132394 Sur la diagonale d’Alexander-Whitney On the Alexander-Whitney diagonal.

[7] J. Sánchez-Guevara, About E-infinity structures in L-Algebras. Tesis doct. Paris: Université Paris VII, (2016). url: www.theses.fr/2016USPCC204.

[8] J. Sánchez-Guevara, E-infinity coalgebra structure on chain complexes with integer coefficients. Revista Colombiana de Matem´aticas 55(2021), 197-203. doi: 10.15446/recolma.v55n2.102690

[9] J. Sánchez -Guevara, Operads libres sobre módulos diferenciales graduados. Revista de Matemática: Teoría y Aplicaciones 29(2021), no. 1, 19-37. doi: 10.15517/rmta.v29i1.41404

[10] J. D. Stasheff, Homotopy associativity of H-Spaces. I. Transactions of the American Mathematical Society 108(1963), no. 2, 275-292. doi: 10.2307/1993608

[11] J. D. Stasheff, Homotopy associativity of H-Spaces. II. Transactions of the American Mathematical Society 108(1963), no. 2, 293-312. doi: 10.2307/ 1993609

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Published

2025-07-24

How to Cite

Extension of an operad structure defined on a sub-S-modules. (2025). Revista De Matemática: Teoría Y Aplicaciones, 32(2), 117-136. https://doi.org/10.15517/9na6rv61