API reference
This appendix is a map of the principal public operations in TensorCategories.jl. It is deliberately curated: the package uses Julia's multiple dispatch, so an exported generic function need not have a method for every category model. The mathematical chapters state the hypotheses, conventions, and available algorithms for each model. Some interface operations extend OSCAR generics; the tables qualify a name when TensorCategories.jl does not export it itself.
Use Julia's help mode and method table for the exact signatures supported by the installed version:
help?> center
julia> methods(center)The reference is organized by mathematical role.
| Area | Contents |
|---|---|
| Category interface | Categories, objects, morphisms, Hom spaces, additive and abelian operations |
| Tensor structure | Tensor products, duality, braidings, coherence checks, and skeletal fusion data |
| Concrete categories | Realizations by sets, vector spaces, gradings, representations, and sheaves |
| Fusion data and databases | Supplied skeletal categories and data loaders |
| Constructions | Centers, internal modules, group actions, and functors |
| Utilities | Grothendieck rings, numerical conversion, and persistence |
For a linear introduction to the package, begin with models and the category interface. The catalogue records the coefficient fields, conventions, limitations, and references for the supplied category families.