Murat Kasimov

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Я language (β)

/Я language (β)/Primitives/Product/

: ( i `P` ii ) ~ ( Product i ii ) > These : i `AR____` ii `AR___` i `P` ii > `tb` : i `P` i `AR_______` Twice i > `tb` : ii `P` i `AR_______` Along i ii > `tb` : i `AR` ii `P_` i `AR_______` Place i ii > `tb` : i `AR` ii `P_` i `AR_______` Store i ii > `tb` : t i `P` tt i `AR_______` t `P'T'I'TT'I` tt `T'I___` i > `tb` : Supertype ( Nonempty List i ) `P` i `AR______` Nonempty List i > `tb` : List ( Supertype ( Tree i ) ) `P` i `AR______` Tree i > `tb` : Twice ( Supertype ( Tree i ) ) `P` i `AR_____` Binary Tree i > `tb` : List i `P` List i `AR_______` Shafted List i > `tb` : Alone i `P` Shafted List i `AR_______` Scrolling List i > `tb` : List i `P` Shafted List i `AR_______` Sliding List i > `tb` : Supertype ( Construction t i ) `P` i `AR____` Construction t i

Product is a limit of Arrow category:

> `hop` : a `AR_` o `AR_______` a `AR_` oo `AR_______` a `AR_` o `P` oo

Product is a left Adjoint Functor to Arrow Functor in Arrow category:

> `hjd` : i `AR___` ii `AR__` i `P` ii

Covariant Functor from Arrow into Arrow (1/2 argument):

> `yoi` : Product a _ `AR_______` a `AR` o `AR______` Product o _

Covariant Functor from Arrow into Arrow (2/2 argument):

> `yio` : Product _ a `AR_______` a `AR` o `AR______` Product _ o

Covariant Functor from Kleisli Arrow into Kleisli Arrow (1/2 argument):

> `yoikl` : Product a _ `AR_____` a `AR` tt o `AR______` tt ( Product o _ )

Covariant Functor from Kleisli Arrow into Kleisli Arrow (2/2 argument):

> `yiokl` : Product _ a `AR_____` a `AR` tt o `AR______` tt ( Product _ o )

Covariant Functor from Arrow into Arrow with representing objects:

> `yoir` : Product o _ `AR______` Unit `AR` o > `yior` : Product _ o `AR______` Unit `AR` o > `yoor` : Product o o `AR______` Unit `S` Unit `AR` o