• In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified...
    18 KB (2,611 words) - 01:50, 26 March 2025
  • Cartesian closed categories are closed categories. In particular, any topos is closed. The canonical example is the category of sets. Compact closed categories...
    3 KB (348 words) - 12:41, 19 March 2025
  • 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...
    7 KB (1,167 words) - 18:33, 17 September 2023
  • Any category with finite products (a "finite product category") can be thought of as a cartesian monoidal category. In any cartesian monoidal category, the...
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  • Thumbnail for Cartesian product
    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...
    27 KB (3,945 words) - 17:31, 22 April 2025
  • Thumbnail for Category (mathematics)
    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...
    21 KB (2,525 words) - 18:54, 19 March 2025
  • value Inverse limit – Construction in category theory Cartesian closed category – Type of category in category theory Categorical pullback – Most general...
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  • being a Cartesian closed category while still containing all of the typical spaces of interest. This makes CGHaus a particularly convenient category of topological...
    11 KB (1,365 words) - 23:19, 14 May 2025
  • all finite products and exponential objects are called cartesian closed categories. Categories (such as subcategories of Top) without adjoined products...
    8 KB (1,143 words) - 18:49, 9 October 2024
  • Dual (category theory) Groupoid Image (category theory) Coimage Commutative diagram Cartesian morphism Slice category Isomorphism of categories Natural...
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  • a closed category in category theory Cartesian coordinate system, modern rectangular coordinate system Cartesian diagram, a construction in category theory...
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  • Thumbnail for Category theory
    theory, where a cartesian closed category is taken as a non-syntactic description of a lambda calculus. At the very least, category theoretic language...
    34 KB (3,910 words) - 19:56, 5 July 2025
  • bifunctor. Cartesian closed category – Type of category in category theory Limits and colimits in an ∞-category Mac Lane, Saunders (1998). Categories for the...
    27 KB (4,333 words) - 16:33, 22 June 2025
  • is Rel, the category having sets as objects and relations as morphisms, with Cartesian monoidal structure. A symmetric monoidal category ( C , ⊗ , I )...
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  • category, a distributive lattice as a small posetal distributive category, a Heyting algebra as a small posetal finitely cocomplete cartesian closed category...
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  • 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...
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  • Examples include cartesian closed categories such as Set, the category of sets, and compact closed categories such as FdVect, the category of finite-dimensional...
    18 KB (2,436 words) - 07:41, 19 June 2025
  • typed lambda calculus and cartesian closed categories. Under this correspondence, objects of a cartesian-closed category can be interpreted as propositions...
    58 KB (6,386 words) - 00:10, 10 June 2025
  • 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...
    12 KB (1,449 words) - 17:58, 29 March 2025
  • 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...
    64 KB (10,260 words) - 08:58, 28 May 2025
  • 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...
    14 KB (1,986 words) - 16:35, 23 March 2025
  • shortcomings of the category of topological spaces. In particular, under some of the definitions, they form a cartesian closed category while still containing...
    30 KB (4,678 words) - 15:25, 21 April 2025
  • Lambda calculus (category Commons category link from Wikidata)
    objects in the style of the lambda calculus Cartesian closed category – A setting for lambda calculus in category theory Categorical abstract machine – A...
    90 KB (12,117 words) - 02:29, 15 June 2025
  • functions taken as morphisms, and the cartesian product taken as the product, forms a Cartesian closed category. Here, eval (or, properly speaking, apply)...
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  • simply typed lambda calculus, which is the internal language of Cartesian closed categories. Typing rules specify the structure of a typing relation that...
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  • . The category Cat {\displaystyle {\textbf {Cat}}} of all small categories with functors as morphisms is therefore a cartesian closed category. Mathematics...
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  • Lawvere's fixed-point theorem (category Category theory)
    William Lawvere in 1969. Lawvere's theorem states that, for any Cartesian closed category C {\displaystyle \mathbf {C} } and given an object B {\displaystyle...
    3 KB (365 words) - 12:34, 26 May 2025
  • 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...
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  • In category theory, a branch of mathematics, dagger compact categories (or dagger compact closed categories) first appeared in 1989 in the work of Sergio...
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  • objects). Categories that do have both products and internal homs are exactly the closed monoidal categories. The setting of cartesian closed categories is sufficient...
    36 KB (5,036 words) - 09:11, 23 June 2025