Category of finite dimensional Hilbert spaces
Encyclopedia
In mathematics
, the category
FdHilb has all finite dimensional Hilbert spaces for objects and linear transformations between them.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the category
Category (mathematics)
In mathematics, a category is an algebraic structure that comprises "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose...
FdHilb has all finite dimensional Hilbert spaces for objects and linear transformations between them.
Properties
This category- is monoidalMonoidal categoryIn mathematics, a monoidal category is a category C equipped with a bifunctorwhich is associative, up to a natural isomorphism, and an object I which is both a left and right identity for ⊗, again up to a natural isomorphism...
, - possesses finite biproductBiproductIn category theory and its applications to mathematics, a biproduct of a finite collection of objects in a category with zero object is both a product and a coproduct. In a preadditive category the notions of product and coproduct coincide for finite collections of objects...
s, and - is dagger compactDagger compact categoryIn mathematics, dagger compact categories first appeared in 1989 in the work of Doplicher and Roberts on the reconstruction of compact topological group from their category of finite-dimensional continuous unitary representations...
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