Relations between many category theory structures - introductory texts and maps

Question

There are many kinds of category theory structures. What are some good texts and good ways to remember the relations between them? For example, can there be a web of embedding relations between these category theory structures? (where can I find those webs to read.) Like which ones contain the other ones as more general cases. (Intersections and unions between different category theory structures.)

• unitary braided fusion category = unitary premodular category

• unitary fusion category

• unitary symmetric fusion category

• unitary modular category

• monoidal category = tensor category

• spherical fusion category

• modular tensor category

Here are some facts I know of

1.

$$ \text{unitary braided fusion category = unitary premodular category} \supset \left\{ \begin{array}{l} \text{(1) unitary symmetric fusion category}\\ \text{(2) unitary modular category} \end{array} \right. $$

2. The center construction of the spherical fusion category defines a modular tensor category.

Please feel free to make comments and give a list of advice.