BiclosedCategory

class discopy.abc.BiclosedCategory

Bases: MonoidalCategory, Generic

A biclosed category is a MonoidalCategory with methods ev and curry for the evaluation and currying of morphisms.

We also assume the type for objects comes with methods for left and right exponentials :code`x << y` and :code`x >> y`.

abstract classmethod ev(base, exponent, left=True)

The evaluation of an exponential type, to be instantiated.

Parameters:

• base (C0) – The base of the exponential type.

• exponent (C0) – The exponent of the exponential type.

• left (bool) – Whether to take the left or right evaluation.

Return type:

C1

abstract curry(n=1, left=True)

The currying of a morphism, to be instantiated.

Parameters:

• n (int) – The number of objects to curry.

• left (bool) – Whether to curry on the left or right.

Return type:

C1

base_and_exponent(n, left)

The base and exponent that uncurry() evaluates, read off the exponential object in the codomain.

Parameters:

• n (int) – The number of objects to uncurry.

• left (bool) – Whether to uncurry on the left or right.

Return type:

tuple[C0, C0]

uncurry(n=1, left=True)

Uncurry a morphism by composing it with ev(), assuming its codomain is an exponential object. If the exponent has less than n objects, we uncurry the remaining ones in turn.

Parameters:

• n (int) – The number of objects to uncurry.

• left (bool) – Whether to uncurry on the left or right.

Return type:

C1