Compact closed category information

In category theory, a branch of mathematics, compact closed categories are a general context for treating dual objects. The idea of a dual object generalizes...

closed categories are closed categories. In particular, any topos is closed. The canonical example is the category of sets. Compact closed categories...

In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified...

in category theory, a closed monoidal category (or a monoidal closed category) is a category that is both a monoidal category and a closed category in...

In category theory, a branch of mathematics, dagger compact categories (or dagger compact closed categories) first appeared in 1989 in the work of Sergio...

include cartesian closed categories such as Set, the category of sets, and compact closed categories such as FdVect, the category of finite-dimensional...

point of X has a compact neighbourhood. 2. every point of X has a closed compact neighbourhood. 2′. every point of X has a relatively compact neighbourhood...

replace compact spaces with compact Hausdorff spaces. Compactly generated spaces were developed to remedy some of the shortcomings of the category of topological...

Bob (2016), "Reasoning about meaning in natural language with compact closed categories and Frobenius algebras", Logic and Algebraic Structures in Quantum...

space every point has a local base of closed compact neighborhoods; and (2) in a compact space any collection of closed sets with the finite intersection...

category. An autonomous category that is also symmetric is called a compact closed category. Any endomorphism f of a dualizable object admits a trace, which...

if countable unions of closed sets with empty interior also have empty interior. According to the Baire category theorem, compact Hausdorff spaces and complete...

ordered categories with involution, Journal of Pure and Applied Algebra 143 (1999), No.1–3, 293–307 P. Selinger, Dagger compact closed categories and completely...

the category of finite-dimensional Hilbert spaces if and only if it can be proved in the graphical language of dagger compact closed categories. Dagger...

symmetric monoidal category that is also compact closed is a dagger compact category; both of the above examples are in fact dagger compact. Mathematics portal...

mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff. Locally compact groups are important...

symmetric is called a compact closed category. A monoidal category is a category with a tensor product, precisely the sort of category for which rigidity...

product and a coproduct, the tensor product, which makes FinVect a compact closed category. Tensor networks are string diagrams interpreted in FinVect. Group...

monoidal category, the existence of left duals is equivalent to the existence of right duals, categories of this kind are called (symmetric) compact closed categories...

Archived from the original on 2017-02-02. Retrieved 2017-01-26. See Compact closed category. Hungerford, Thomas W. (1974). Algebra. Springer. ISBN 0-387-90518-9...

closed subset. Equivalently, it is a relatively open subset of its closure. Locally compact A space is locally compact if every point has a compact neighbourhood:...

space where the image of every continuous map from a compact Hausdorff space into the space is closed. In particular, every Hausdorff space is weak Hausdorff...

category of compactly generated weak Hausdorff spaces CGWH is one of typically used categories in algebraic topology as a substitute for the category...

the category of topological spaces fails to be cartesian closed. However, the category of locally compact topological spaces is not cartesian closed either...

morphisms or with the category of compactly generated weak Hausdorff spaces. Like many categories, the category Top is a concrete category, meaning its objects...

category Triangulated category Model category 2-category Dagger symmetric monoidal category Dagger compact category Strongly ribbon category Closed monoidal...

total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. A totally bounded set can be covered by...

the symmetry of the monoidal category). Every compact closed category admits a trace. Given a traced monoidal category C, the Int construction generates...