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Generalized information structures and their cohomology. (arXiv:1709.07807v2 [cs.IT] UPDATED)
来源于:arXiv
D. Bennequin and P. Baudot introduced a cohomological construction adapted to
information theory, called 'information cohomology', that characterizes Shannon
entropy through a cocycle condition. This text develops the relation between
information cohomology and topos theory. We also introduce several new
constructions and results. First, we define generalized information structures,
as categories of finite random variables related by a notion of extension or
refinement; classical and quantum probability spaces appear as models
(representations) for these general structures. Generalized information
structures form a category with finite products and coproducts. We prove that
information cohomology is invariant under isomorphisms of generalized
structures. Secondly, we prove that the relatively-free bar construction gives
a projective object for the computation of cohomology. Thirdly, we provide
detailed computations of $H^1$ for classical probabilities and describe the
degenerate cases. 查看全文>>