The Motivation

This package began its journey asking the question "Can we play around with explicit categorical entities in the computer?".

By nature categorical operations and constructions are very generic and can be applied as long as the objects (or morphisms) are fitting. TensorCategories.jl provides an interface for categories with additional structure, precisely additive, linear, abelian, monoidal, tensor and fusion categories.

Realizing Categories in The Computer

Due to the nature of category theory the realization of certain categories is very dependent on themselves. Thus the internal workings are generally up to the developer. As long as the interface for the desired additional structures is implemented.

Some kind of categories, i.e. fusion categories, are entirely described (up to equivalence) by discrete data known as $6j$-symbols$. Thus for such categories we can provide a datatype SixJCategory to quickly work with categories given by such data.

Mathematical Foundation

Throughout the package we will consider definitions and terminology as provided in [1].