License | BSD-style (see the file LICENSE) |
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Maintainer | sjoerd@w3future.com |
Stability | experimental |
Portability | non-portable |
Safe Haskell | Safe |
Language | Haskell2010 |
Category
class Category k where Source #
An instance of Category k
declares the arrow k
as a category.
Category (->) Source # | The category with Haskell types as objects and Haskell functions as arrows. |
Category Cat Source # |
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Category Unit Source # |
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Category Void Source # |
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Category AdjArrow Source # | The category with categories as objects and adjunctions as arrows. |
Category Boolean Source # |
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Category Simplex Source # | The (augmented) simplex category is the category of finite ordinals and order preserving maps. |
Category Cube Source # | |
Category k => Category (Op k) Source # |
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Category (f (Fix f)) => Category (Fix f) Source # |
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Category (Kleisli m) Source # | The category of Kleisli arrows. |
(Category c1, Category c2) => Category ((:**:) c1 c2) Source # | The product category of category |
Category d => Category (Nat c d) Source # | Functor category D^C. Objects of D^C are functors from C to D. Arrows of D^C are natural transformations. |
(Category c1, Category c2) => Category ((:>>:) c1 c2) Source # | The directed coproduct category of categories |
(Category c1, Category c2) => Category ((:++:) c1 c2) Source # | The coproduct category of categories |
Category (MonoidAsCategory f m) Source # | A monoid as a category with one object. |
Category (Dialg f g) Source # | The category of (F,G)-dialgebras. |
(Category (Dom t), Category (Dom s)) => Category ((:/\:) t s) Source # | The comma category T \downarrow S |
Whenever objects are required at value level, they are represented by their identity arrows.
Opposite category
Category k => Category (Op k) Source # |
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HasBinaryProducts k => HasBinaryCoproducts (Op k) Source # | Binary products are the dual of binary coproducts. |
HasBinaryCoproducts k => HasBinaryProducts (Op k) Source # | Binary products are the dual of binary coproducts. |
HasTerminalObject k => HasInitialObject (Op k) Source # | Terminal objects are the dual of initial objects. |
HasInitialObject k => HasTerminalObject (Op k) Source # | Terminal objects are the dual of initial objects. |
Category k => CartesianClosed (Presheaves k) Source # | The category of presheaves on a category |
type InitialObject (Op k) Source # | |
type TerminalObject (Op k) Source # | |
type BinaryCoproduct (Op k) x y Source # | |
type BinaryProduct (Op k) x y Source # | |
type Exponential (Presheaves k) y z Source # | |