2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111640Based on the computation of the third author we obtain an interpretation of the third Mac Lane cohomology of rings using certain kind of crossed extensions of rings in the quadratic world. Actually we obtain two such interpretations corresponding to the two monoidal structures on the category of square groupsK-Theory and HomologyAlgebraic Topology19D55, 18H15, 18D05, 55P43text