منابع مشابه
Quantum Logic in Dagger Kernel Categories
This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of interest, such as categories of relations, partial injections, Hilbert spaces (also modulo phase), and Boolean algebras, and (2) have interesting categori...
متن کاملQuantum Logic in Dagger Categories with Kernels
This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of interest, such as categories of relations, partial injections, Hilbert spaces (also modulo phase), and Boolean algebras, and (2) have interesting categori...
متن کاملOrthomodular lattices, Foulis Semigroups and Dagger Kernel Categories
This paper is a sequel to [19] and continues the study of quantum logic via dagger kernel categories. It develops the relation between these categories and both orthomodular lattices and Foulis semigroups. The relation between the latter two notions has been uncovered in the 1960s. The current categorical perspective gives a broader context and reconstructs this relationship between orthomodula...
متن کاملMonads on Dagger Categories
The theory of monads on categories equipped with a dagger (a contravariant identity-on-objects involutive endofunctor) works best when all structure respects the dagger: the monad and adjunctions should preserve the dagger, and the monad and its algebras should satisfy the so-called Frobenius law. Then any monad resolves as an adjunction, with extremal solutions given by the categories of Kleis...
متن کاملDagger Categories of Tame Relations
Within the context of an involutive monoidal category the notion of a comparison relation cp : X ⊗X → Ω is identified. Instances are equality = on sets, inequality ≤ on posets, orthogonality ⊥ on orthomodular lattices, non-empty intersection on powersets, and inner product 〈− |−〉 on vector or Hilbert spaces. Associated with a collection of such (symmetric) comparison relations a dagger category...
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ژورنال
عنوان ژورنال: Order
سال: 2010
ISSN: 0167-8094,1572-9273
DOI: 10.1007/s11083-010-9145-5