2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64810Taylor presented an explicit resolution for arbitrary monomial ideals. Later, Lyubeznik found that already a subcomplex defines a resolution. We show that the Taylor resolution may be obtained by repeated application of the Schreyer Theorem from the theory of Grobner bases, whereas the Lyubeznik resolution is a consequence of Buchberger's chain criterion. Finally, we relate Froberg's contracting homotopy for the Taylor complex to normal forms with respect to our Grobner bases and use it to derive a splitting homotopy that leads to the Lyubeznik complex.14 pages, to appear in Journal of Symbolic ComputationCommutative AlgebraAlgebraic Geometry13P10text