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** Draft Version ** To any boolean topos one can associate its category ofinternal Hilbert spaces, and if the topos is locally separated one can considera full subcategory of square integrable Hilbert spaces. In both case it is asymmetric monoidal monotone complete $C^{*}$-category. We will prove that anyboolean locally separated topos can be reconstructed as the classifying toposof "non-degenerate" monoidal normal $*$-representations of both its category ofinternal Hilbert spaces and its category of square integrable Hilbert spaces.This suggest a possible extension of the usual Gelfand duality between a classof toposes (or more generally localic stacks or localic groupoids) and a classof symmetric monoidal $C^{*}$-categories yet to be discovered.

Toward a non-commutative Gelfand duality: Boolean locally separated toposes and Monoidal monotone complete $C^{*}$-categories