  With an explicit, algebraic indexing $(2,1)$-category, we develop an
efficient homotopy theory of cyclonic objects: circle-equivariant objects
relative to the family of finite subgroups. We construct an $\infty$-category
of cyclotomic spectra as the homotopy fixed points of an action of the
multiplicative monoid of the natural numbers on the category of cyclonic
spectra. Finally, we elucidate and prove a conjecture of Kaledin on cyclotomic
complexes.
