2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138756An algebraic version of a theorem due to Quillen is proved. More precisely, for a ground field k we consider the motivic stable homotopy category SH(k) of P^1-spectra equipped with the symmetric monoidal structure described in arXiv:0709.3905v1 [math.AG]. The algebraic cobordism P^1-spectrum MGL is considered as a commutative monoid equipped with a canonical orientation. For a commutative monoid E in the category SH(k) we identify the set of monoid homomorphisms from MGL to E in the motivic stable homotopy category with the set of all orientations of E. This result was stated originally in a slightly different form by G. Vezzosi in arXiv:math/0004050v2 [math.AG].LaTeX, 14 pages, uses XY-picAlgebraic GeometryAlgebraic Topology14F05; 55N22; 55P43text