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...

a closed category in category theory Cartesian coordinate system, modern rectangular coordinate system Cartesian diagram, a construction in category theory...

Any category with finite products (a "finite product category") can be thought of as a cartesian monoidal category. In any cartesian monoidal category, the...

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

Dual (category theory) Groupoid Image (category theory) Coimage Commutative diagram Cartesian morphism Slice category Isomorphism of categories Natural...

product; thus any category with a Cartesian product (and a final object) is a Cartesian closed category. In graph theory, the Cartesian product of two graphs...

value Inverse limit – Construction in category theory Cartesian closed category – Type of category in category theory Categorical pullback – Most general...

being a Cartesian closed category while still containing all of the typical spaces of interest. This makes CGHaus a particularly convenient category of topological...

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

and CPO, the category of complete partial orders with Scott-continuous functions. A topos is a certain type of cartesian closed category in which all...

{\displaystyle \operatorname {Hom} } bifunctor. Cartesian closed category – Type of category in category theory Equaliser (mathematics) – Set of arguments...

all finite products and exponential objects are called cartesian closed categories. Categories (such as subcategories of Top) without adjoined products...

theory, where a cartesian closed category is taken as a non-syntactic description of a lambda calculus. At the very least, category theoretic language...

equivalence F is an exact functor. C is a cartesian closed category (or a topos) if and only if D is cartesian closed (or a topos). Dualities "turn all concepts...

in category theory, where it is right adjoint to currying in closed monoidal categories. A special case of this are the Cartesian closed categories, whose...

to the corresponding free categories: F : Quiv → Cat Cat has all small limits and colimits. Cat is a Cartesian closed category, with exponential D C {\displaystyle...

typed lambda calculus and cartesian closed categories. Under this correspondence, objects of a cartesian-closed category can be interpreted as propositions...

category, a distributive lattice as a small posetal distributive category, a Heyting algebra as a small posetal finitely cocomplete cartesian closed category...

shortcomings of the category of topological spaces. In particular, under some of the definitions, they form a cartesian closed category while still containing...

non-examples of symmetric monoidal categories: The category of sets. The tensor product is the set theoretic cartesian product, and any singleton can be...

. The category Cat {\displaystyle {\textbf {Cat}}} of all small categories with functors as morphisms is therefore a cartesian closed category. Mathematics...

William Lawvere in 1969. Lawvere's theorem states that, for any Cartesian closed category C {\displaystyle \mathbf {C} } and given an object B {\displaystyle...

functions taken as morphisms, and the cartesian product taken as the product, forms a Cartesian closed category. Here, eval (or, properly speaking, apply)...

the indiscrete category on that set. Exponential object. In a cartesian closed category the endofunctor C → C given by –×A has a right adjoint –A. This...

objects). Categories that do have both products and internal homs are exactly the closed monoidal categories. The setting of cartesian closed categories is sufficient...

theory Directed complete partial order Knaster–Tarski theorem Cartesian closed category Yoneda lemma Graph reduction Combinator graph reduction Strict...

(of a given type) that have Cartesian products is called a Cartesian category. Many of these are Cartesian closed categories. Sets are an example of such...

analogy, are categories enriched over (FinSet, ×), the category of finite sets with Cartesian product as the monoidal operation. If C is a closed monoidal...

A category is said to be locally cartesian closed if every slice of it is cartesian closed (see above for the notion of slice). Locally cartesian closed...