Diagram

class discopy.balanced.Diagram(inside, dom, cod, _scan=True)

Bases: discopy.braided.Diagram, discopy.traced.Diagram

A balanced diagram is a braided diagram with Twist.

Parameters:

• inside (Layer) – The layers inside the diagram.

• dom (monoidal.Ty) – The domain of the diagram, i.e. its input.

• cod (monoidal.Ty) – The codomain of the diagram, i.e. its output.

Note

By default, our balanced diagrams are traced. Although not every balanced category embeds faithfully into a traced one (see the nLab), the free balanced category does have the desired cancellation property and it does in fact embed faithfully into the free balanced traced category.

classmethod twist(dom)

The twist on an object.

Parameters:

dom (Ty) – The domain of the twist.

Return type:

Diagram

Note

This calls twist_factory.

to_braided()

Doubles evry object and sends the twist to the braid.

Example

>>> x = Ty('x')
>>> braided_twist = Diagram.twist(x).to_braided()

>>> from discopy.drawing import Equation
>>> Equation(Twist(x), braided_twist, symbol='$\\mapsto$').draw(
...     wire_labels=False,
...     path="docs/_static/balanced/twist_dual_rail.png")

braid_factory

alias of Braid

factory

alias of Diagram

sum_factory

alias of Sum

trace_factory

alias of Trace

twist_factory

alias of Twist