A dedicated global model structure for K-linear ∞-local systems is constructed via simplicial chain complexes, monoidal for base 1-types under the external tensor product.
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Hermitian forms on Hilbert spaces arise from the monoid structure of complex conjugation in Z/2-equivariant real linear types within LHoTT, requiring only a negative unit term.
A parity concept for invertible morphisms yields a coherence theorem in symmetric monoidal categories, with the free permutative category on an invertible generator equivalent to the super integers via ±1.
The pushout of entangled and parameterized quantum information in monoidal categories yields the external tensor product on flat K-theory bundles.
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A Global Model Structure for $\mathbb{K}$-Linear $\infty$-Local Systems
A dedicated global model structure for K-linear ∞-local systems is constructed via simplicial chain complexes, monoidal for base 1-types under the external tensor product.
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Quantum and Reality
Hermitian forms on Hilbert spaces arise from the monoid structure of complex conjugation in Z/2-equivariant real linear types within LHoTT, requiring only a negative unit term.
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Invertibility and parity in symmetric monoidal categories
A parity concept for invertible morphisms yields a coherence theorem in symmetric monoidal categories, with the free permutative category on an invertible generator equivalent to the super integers via ±1.
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Entanglement of Sections: The pushout of entangled and parameterized quantum information
The pushout of entangled and parameterized quantum information in monoidal categories yields the external tensor product on flat K-theory bundles.