**Abstract:** Since the 50's of the last century, Eckman observed that the existence of n-medias over certain topological spaces (polyhedra) is closely related to its homotopic structure. He uses the functors of homotopy and singular homology groups to characterize compact polyhedra that have an n-media. Surprisingly, and independently of Professor Eckman, economists Chichilnisky and Heal use these same techniques in the 1980s to solve problems arising from social choice theory. In this talk I will show the functors between certain categories that are derived from Top and Grp that I have used in obtaining recent results on social choice functions.

**Curriculum vitae:** Academic Training: Postdoctoral Stay: From August 2011 to July 2013, he was on a postdoctoral stay at FCFM-BUAP under the direction of Dr. Oleg Okunev. Doctorate: On August 12, 2010 at the Faculty of Sciences of the UNAM, he obtained the degree of Doctor of Science (Mathematics) presenting the thesis Own Actions and Dimension which was directed by Dr. Sergey Antonyan. Master: On November 26, 2004 at the Faculty of Sciences of the UNAM, he obtained the Master's degree in Science (Mathematics) presenting the thesis Subcategories Excisible and Coescindibles which was directed by Dr. Francisco Marmolejo Rivas. Bachelor of Mathematics: On February 25, 2002 at the Faculty of Physical-Mathematical Sciences of the Benemérita Autonomous University of Puebla, I obtained the degree of Bachelor of Mathematics presenting the thesis Functores Reflectores and the Theories of Form which was directly by Dr Alexander Bykov Teaching Experience: Associate Curriculum Professor in the Mathematics Department of the UAM-I of the 2014-I quarter to date. Two degree thesis directed. Five research articles published in journals of high international impact. Member of the National System of Researchers Level I in the period 2017-2019. Areas of interest for research: Topological Groups of Transformations; Topological Algebra; Categorical Methods in Topology and Algebra; Topological Methods Applied to Economics and Game Theory.