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Control.Category.Cartesian | Portability | non-portable (class-associated types) | Stability | experimental | Maintainer | Edward Kmett <ekmett@gmail.com> |
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Description |
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Synopsis |
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Documentation |
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module Control.Category.Associative |
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module Control.Category.Monoidal |
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Pre-(Co)Cartesian categories
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NB: This is weaker than traditional category with products! That is Cartesian, below.
The problem is (->) lacks an initial object, since every type is inhabited in Haskell.
Consequently its coproduct is merely a semigroup, not a monoid as it has no identity, and
since we want to be able to describe its dual category, which has this non-traditional
form being built over a category with an associative bifunctor rather than as a monoidal category
for the product monoid.
Minimum definition:
fst, snd, diag
fst, snd, (&&&)
| | Methods | | | | | | | (&&&) :: k a b -> k a c -> k a (p b c) | Source |
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free construction of Bifunctor for the product Bifunctor Prod k if (&&&) is known
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free construction of Braided for the product Bifunctor Prod k
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free construction of Associative for the product Bifunctor Prod k
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free construction of Coassociative for the product Bifunctor Prod k
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| Methods | | | | | | | (|||) :: k a c -> k b c -> k (s a b) c | Source |
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free construction of Bifunctor for the coproduct Bifunctor Sum k if (|||) is known
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free construction of Braided for the coproduct Bifunctor Sum k
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free construction of Associative for the coproduct Bifunctor Sum k
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free construction of Coassociative for the coproduct Bifunctor Sum k
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(Co)Cartesian categories
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Produced by Haddock version 2.4.2 |