In the mathematical field of
category theory, a dagger symmetric monoidal category is a
monoidal category
In mathematics, a monoidal category (or tensor category) is a category \mathbf C equipped with a bifunctor
:\otimes : \mathbf \times \mathbf \to \mathbf
that is associative up to a natural isomorphism, and an object ''I'' that is both a left ...
that also possesses a
dagger structure. That is, this category comes equipped not only with a
tensor product
In mathematics, the tensor product V \otimes W of two vector spaces and (over the same Field (mathematics), field) is a vector space to which is associated a bilinear map V\times W \to V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an e ...
in the
category theoretic sense but also with a
dagger structure, which is used to describe
unitary morphisms and
self-adjoint morphisms in
: abstract analogues of those found in FdHilb, the
category of finite-dimensional Hilbert spaces. This type of
category
Category, plural categories, may refer to:
Philosophy and general uses
*Categorization, categories in cognitive science, information science and generally
* Category of being
* ''Categories'' (Aristotle)
* Category (Kant)
* Categories (Peirce) ...
was introduced by Peter Selinger
as an intermediate structure between
dagger categories and the
dagger compact categories that are used in
categorical quantum mechanics
Categorical quantum mechanics is the study of quantum foundations and quantum information using paradigms from mathematics and computer science, notably monoidal category theory. The primitive objects of study are physical processes, and the diff ...
, an area that now also considers dagger symmetric monoidal categories when dealing