frobenius#

The free hypergraph category, i.e. diagrams with swaps and spiders.

Spiders are also known as dagger special commutative Frobenius algebras.

Summary#

Ob

A frobenius object is a self-dual pivotal object.

Ty

A frobenius type is a pivotal type with frobenius objects inside.

Diagram

A frobenius diagram is a compact diagram with Spider boxes.

Box

A frobenius box is a compact box in a frobenius diagram.

Cup

A frobenius cup is a compact cup in a frobenius diagram.

Cap

A frobenius cap is a compact cap in a frobenius diagram.

Swap

A frobenius swap is a compact swap in a frobenius diagram.

Spider

The spider with n_legs_in and n_legs_out on a given atomic type, with some optional phase as data.

Category

A hypergraph category is a compact category with a method spiders.

Functor

A hypergraph functor is a compact functor that preserves spiders.