Category whose hom objects correspond (di-)naturally to objects in itself
In category theory, a branch of mathematics, a closed category is a special kind of category.
In a locally small category, the external hom (x, y) maps a pair of objects to a set of morphisms. So in the category of sets, this is an object of the category itself. In the same vein, in a closed category, the (object of) morphisms from one object to another can be seen as lying inside the category. This is the internal hom [x, y].
Every closed category has a forgetful functor to the category of sets, which in particular takes the internal hom to the external hom.
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 branch of mathematics, a closedcategory is a special kind of category. In a locally small category, the external hom (x, y) maps...
in category theory, a closed monoidal category (or a monoidal closedcategory) is a category that is both a monoidal category and a closedcategory in...
(abbreviated as POS or PoS, also known as word class or grammatical category) is a category of words (or, more generally, of lexical items) that have similar...
In category theory, a branch of mathematics, compact closedcategories are a general context for treating dual objects. The idea of a dual object generalizes...
Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the...
different application, for which monoidal categories can be considered an abstraction, is a system of data types closed under a type constructor that takes...
to the corresponding free categories: F : Quiv → Cat Cat has all small limits and colimits. Cat is a Cartesian closedcategory, with exponential D C {\displaystyle...
The four categories are: Category A, B and C prisons are called closed prisons, whereas category D prisons are called open prisons. Category A prisoners...
"[came] off as caricatures". The Case Closed manga series was awarded the 46th Shogakukan Manga Award in the shōnen category in 2001. It respondents in an online...
In category theory, a branch of mathematics, a symmetric monoidal category is a monoidal category (i.e. a category in which a "tensor product" ⊗ {\displaystyle...
closed model categories is sometimes thought of as homotopical algebra. The definition given initially by Quillen was that of a closed model category...
In category theory, a branch of mathematics, dagger compact categories (or dagger compact closedcategories) first appeared in 1989 in the work of Sergio...
abelian categories is closed under several categorical constructions, for example, the category of chain complexes of an abelian category, or the category of...
In category theory, a branch of abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories...
In category theory, a branch of mathematics, a functor category D C {\displaystyle D^{C}} is a category where the objects are the functors F : C → D {\displaystyle...
category symmetric monoidal or even symmetric closed monoidal, respectively).[citation needed] Enriched category theory thus encompasses within the same framework...
space if countable unions of closed sets with empty interior also have empty interior. According to the Baire category theorem, compact Hausdorff spaces...
specifically category theory, a posetal category, or thin category, is a category whose homsets each contain at most one morphism. As such, a posetal category amounts...
have special permits to enter such areas. The locations of the first category of closed cities were chosen for their geographical characteristics. They were...
obvious example of a preadditive category is the category Ab itself. More precisely, Ab is a closed monoidal category. Note that commutativity is crucial...
In category theory, a branch of mathematics, a dagger category (also called involutive category or category with involution) is a category equipped with...
UEFA stadium categories are categories for football stadiums laid out in UEFA's Stadium Infrastructure Regulations. Using these regulations, stadiums...
In mathematics, a comma category (a special case being a slice category) is a construction in category theory. It provides another way of looking at morphisms:...
in theaters. Cinema captioning falls into the categories of open and closed. The definition of "closed" captioning in this context is different from television...
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