Abstract
The category P(A) h of hermitian modules is symmetric monoidal. The hyperbolic functor from P(A) to P(A) h induces a morphism between the classifying spaces BS −1S and BS h − 1 S h of their K-theories. If 2 is invertible, then there exists a category W ( P ( A ) h ) whose classifying space fits in a homotopy fibration B S − 1 → H * B S h − 1 S h → B W ( P ( A ) h ) . This homotopy fibration generalizes to the case of a “hermitian additive category” C h (associated to an additive category C with a duality functor t ). Furthermore, we define the K-theory ℒ(C h ) of a “hermitian exact category” C h which fits in a homotopy fibration Ω B Q ( C ) → B ℒ ( C h ) → B W ( C h ) . Then we show that this generalizes our previous homotopy fibration for additive categories when all short exact sequences in C split.
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