2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63331We determine the L-S category of Sp(3) by showing that the 5-fold reduced diagonal $\widebarΔ_5$ is given by $ν^2$, using a Toda bracket and a generalised cohomology theory $h^*$ given by $h^*(X,A) = \{X/A,{\mathbb S}[0,2]\}$, where ${\mathbb S}[0,2]$ is the 3-stage Postnikov piece of the sphere spectrum ${\mathbb S}$. This method also yields a general result that $\cat(Sp(n)) \geq n+2$ for $n \geq 3$, which improves the result of Singhof.12 pagesAlgebraic Topology55M30; 55N20, 22E20text