Introduces weak partial monoids and simplicial effects, and claims a new simplicial effect beyond effect algebroids whose states match all density operators.
Cohomology of Effect Algebras
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We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Kunneth and Mayer-Vietoris sequences. The second way involves a chain complex of ordered abelian groups, and gives rise to a cohomological characterization of state extensions on effect algebras. This has applications to no-go theorems in quantum foundations, such as Bell's theorem.
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Simplicial effects and weakly associative partial groups
Introduces weak partial monoids and simplicial effects, and claims a new simplicial effect beyond effect algebroids whose states match all density operators.