abc

Contents

abc#

The abstract base classes for categories.

These mirror the concrete hierarchy of discopy modules: each class adds the characteristic generator of its categorical structure as an abc.abstractmethod(), e.g. BraidedCategory is a MonoidalCategory with an abstract BraidedCategory.braid().

Summary#

`Category`	A category is a Python class with methods `dom, cod, id, then`, together with an attribute `ob` for its objects.
`MonoidalCategory`	A monoidal category is a `Category` with a method `tensor` for both its objects and its arrows.
`BraidedCategory`	A braided category is a `MonoidalCategory` with a method `braid` for the natural isomorphism `x @ y -> y @ x`.
`TracedCategory`	A traced category is a `MonoidalCategory` with a method `trace` for the partial trace of a morphism over some objects.
`BalancedCategory`	A balanced category is a `BraidedCategory` and a `TracedCategory` with a method `twist` for the natural automorphism `x -> x`.
`SymmetricCategory`	A symmetric category is a `BalancedCategory` where the braid is its own inverse called `swap` for the symmetry `x @ y -> y @ x`.
`MarkovCategory`	A Markov category is a `SymmetricCategory` with methods `copy` and `merge` for the supply of commutative comonoids.
`FeedbackCategory`	A feedback category is a `MarkovCategory` with a `delay` endofunctor and a `feedback` operator.
`ClosedCategory`	A closed category is a symmetric `BiclosedCategory`.
`RigidCategory`	A rigid category is a `BiclosedCategory` where every object has a left and right adjoint, witnessed by methods `cups` and `caps`.
`PivotalCategory`	A pivotal category is a `RigidCategory` where the left and right adjoints coincide, hence it is also a `TracedCategory`.
`RibbonCategory`	A ribbon category is a `PivotalCategory` which is also a `BalancedCategory`, i.e. where diagrams can draw knots and links.
`NamedGeneric`	A `NamedGeneric` is a `Generic` where the type parameter has a name.