Diagram#

class discopy.balanced.Diagram(inside, dom, cod, _scan=True)[source]#

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)[source]#

The twist on an object.

Parameters:: dom (Ty) – The domain of the twist.
Return type:: Diagram

Note

This calls twist_factory.

to_braided()[source]#

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(
...     draw_type_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

Diagram

Contents

Diagram#