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Abstract view

Lusternik-Schnirelmann category and algebraic $R$-local homotopy theory

In this paper, we define the notion of $R_{\ast}$-$\LS$ category associated to an increasing system of subrings of $\Q$ and we relate it to the usual $\LS$-category. We also relate it to the invariant introduced by F\'elix and Lemaire in tame homotopy theory, in which case we give a description in terms of Lie algebras and of cocommutative coalgebras, extending results of Lemaire-Sigrist and F\'elix-Halperin.