Relations between many category theory structures – introductory texts

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.

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

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