# 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.feedback` The free feedback category, i.e. diagrams with delayed feedback loops. `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.