We present the Bogoliubov theory for the Bose-Einstein condensation of Feshbach molecules in a balanced\ud Fermi mixture. Because the Bogoliubov theory includes (Gaussian) fluctuations, we can in this manner accurately\ud incorporate both the two-body and many-body aspects of the BEC-BCS crossover that occurs near a\ud Feshbach resonance. We apply the theory in particular to the very broad Feshbach resonance in atomic 6Li at\ud a magnetic field of B0=834 G and find good agreement with experiments in that case. The BEC-BCS crossover\ud for more narrow Feshbach resonances is also discussed
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