  Let $X$ be a finite type simply connected rationally elliptic CW-complex with
Sullivan minimal model $(\Lambda V, d)$ and let $k\geq 2$ the biggest integer
such that $d=\sum_{i\geq k}d_i$ with $d_i(V)\subseteq \Lambda ^iV$. We show
that: $cat(X_{\mathbb{Q}}) = depht(\Lambda V, d_k)$ if and only if $(\Lambda
V,d_{k})$ is elliptic. This result is obtained by introducing tow new spectral
sequences that generalize the Milnor-Moore spectral sequence and its
$\mathcal{E}xt$-version \cite{Mur94}. As a corollary, we recover a known result
proved - with different methods - by L. Lechuga and A. Murillo in \cite{LM02}
and G. Lupton in \cite{Lup02}: If $(\Lambda V,d_{k})$ is elliptic, then
$cat(X_{\mathbb{Q}}) = dim(\pi_{odd}(X)\otimes\mathbb{Q}) +
(k-2)dim(\pi_{even}(X)\otimes\mathbb{Q})$. In the case of a field ${IK}$ of
$char({IK})=p$ (an odd prim) we obtain an algebraic approach for $e_{IK}(X)$
where $X$ is an $r$-connected ($r\geq 1$) finite CW-complex such that $p>
dim(X)/r$.
