A dagger symmetric monoidal category is a monoidal category which also possesses a dagger structure; in other words, it means that this category comes equipped not only with a tensor in the category theoretic sense but also with dagger structure which is used to describe unitary morphism and self-adjoint morphisms in that is, a form of abstract analogues of those found in FdHilb, the category of finite dimensional Hilbert spaces. This type of category was introduced by Selinger as an intermediate structure between dagger categories and the dagger compact categories that are used in categorical quantum mechanics, an area which now also considers dagger symmetric monoidal categories when dealing with infinite dimensional quantum mechanical concepts.
Read more about Dagger Symmetric Monoidal Category: Formal Definition, Examples
Famous quotes containing the words dagger and/or category:
“Cruel with guilt, and daring with despair,
The midnight murderer bursts the faithless bar;
Invades the sacred hour of silent rest
And leaves, unseen, a dagger in your breast.”
—Samuel Johnson (1709–1784)
“The truth is, no matter how trying they become, babies two and under don’t have the ability to make moral choices, so they can’t be “bad.” That category only exists in the adult mind.”
—Anne Cassidy (20th century)