balanced

The free balanced category, i.e. diagrams with braids and a twist.

Summary

Diagram	A balanced diagram is a braided diagram with Twist.
Box	A braided box is a monoidal box in a braided diagram.
Braid	Braid in a balanced category.
Twist	The twist on atomic type dom.
Sum	A balanced sum is a braided sum and a balanced box.
Category	A braided category is a monoidal category with a method braid.
Functor	A balanced functor is a braided functor that twists.

Axioms

The axiom for the twist holds on the nose.

>>> x, y = Ty('x'), Ty('y')
>>> assert Diagram.twist(x @ y) == (Braid(x, y)
...     >> Twist(y) @ Twist(x) >> Braid(y, x))
>>> Diagram.twist(x @ y).draw(path="docs/_static/balanced/twist.png")