syntax

syntax#

DisCoPy’s mathematical core: a zoo of diagrams, categories and functors.

discopy.cat

The free (dagger) category with formal sums, unary operators and symbolic variables.

discopy.monoidal

The free (pre)monoidal category, i.e. planar diagrams.

discopy.braided

The free braided category, i.e. diagrams with braids.

discopy.balanced

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

discopy.symmetric

The free symmetric category, i.e. diagrams with swaps.

discopy.markov

The free Markov category, i.e. a semicartesian category with a supply of commutative comonoid, see Fritz and Liang [FL23].

discopy.traced

The free traced category, i.e. diagrams where outputs can feedback into inputs.

discopy.closed

The free closed monoidal category, i.e. with exponential objects.

discopy.rigid

The free rigid category, i.e. diagrams with cups and caps.

discopy.pivotal

The free pivotal category, i.e. diagrams with cups and caps that can rotate by a full turn.

discopy.ribbon

The free ribbon category, i.e. diagrams with braids, cups and caps.

discopy.compact

The free compact category, i.e. diagrams with swaps, cups and caps.

discopy.frobenius

The free symmetric category with a supply of spiders, also known as special commutative Frobenius algebras.

discopy.hypergraph

The free hypergraph category with cospans of labeled hypergraphs as arrows.

discopy.interaction

The free compact category on a symmetric traced category, or more generally the free ribbon category on a balanced traced category.