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

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