2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/50072The purpose of this paper is to study static solution configuration which describes the magnetic monopoles in a scenary where the gravitation is coupled with Higgs, Yang-Mills and fermions. We are looking for analysis of the energy functional and Bogomol'nyi equations. The Einstein equations now take into consideration the fermions' contribution for energy-momentum tensor. The interesting aspect here is to verify that the fermion field gives a contribution for non abelian magnetic field and for potential which minimise the energy functional.15 pages, AMStexHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext