منابع مشابه
Idempotents in Dagger Categories: (Extended Abstract)
Dagger compact closed categories were studied by Abramsky and Coecke (under the name “strongly compact closed categories”) as an abstract presentation of the category of Hilbert spaces and linear maps, and as a framework in which to carry out the interpretation of quantum protocols. I subsequently showed that dagger compact closed categories can also describe mixed quantum computation, where th...
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...
متن کاملNatural language semantics in biproduct dagger categories
Biproduct dagger categories serve as models for natural language. In particular, the biproduct dagger category of finite dimensional vector spaces over the field of real numbers accommodates both the extensional models of predicate calculus and the intensional models of quantum logic. The morphisms representing the extensional meanings of a grammatical string are translated to morphisms represe...
متن کاملDagger categories and formal distributions
Monoidal dagger categories play a central role in the abstract quantum mechanics of Abramsky and Coecke. The authors show that a great deal of elementary quantum mechanics can be carried out in these categories; for example, the Born rule emerges naturally. In this paper, we construct a category of tame formal distributions with coefficients in a commutative associative algebra and show that it...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2008
ISSN: 1571-0661
DOI: 10.1016/j.entcs.2008.04.021