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Everything about Cartesian closed category
Type of category in category theory
In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming, in that their internal language is the simply typed lambda calculus. They are generalized by closed monoidal categories, whose internal language, linear type systems, are suitable for both quantum and classical computation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Cartesian closed categoryA 5-minute orientation
- Skim a recent paper: A topologically enriched probability monad on the Cartesian closed category of CGWH spacesInfluential work since 2022
- Pick up a classic book: Cartesian meditationsThe most-reprinted book on the subject
- Read the landmark paper: The largest cartesian closed category of domainsCited 78 times
- Go sideways: Exponential objectA closely related topic
- Go sideways: Limit (category theory)A closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The largest cartesian closed category of domains
The category of finite sets and Cartesian closed categories
A note on inconsistencies caused by fixpoints in a cartesian closed category
Cartesian closed categories of algebraic CPOs
Univalence in locally cartesian closed ∞-categories
A cartesian closed category for topology
The category of cauchy spaces is cartesian closed
Generalized Continuous Posets and a New Cartesian Closed Category
🆕 Influential since 2022
A topologically enriched probability monad on the Cartesian closed category of CGWH spaces
Cartesian Closed Double Categories
Cohomology of small Cartesian closed categories
Free Doubly-Infinitary Distributive Categories are Cartesian Closed
Constructing coproducts in locally Cartesian closed $\infty$-categories
📚 Books worth reading
Cartesian meditationsEdmund Husserl, Dorion Cairns · 1960- 📕Cartesian closed categories of domainsA. Jung · 1989
- 📕Cartesian closed categories of domainsAchim Jung · 1988
- 📕Cartesian closed categories of domainsA. Jung · 1989
- 📕Cartesian closed coreflective hullsL. D. Nel · 1970
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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