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.

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