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.
$$
text{unitary braided fusion category = unitary premodular category} supset
left{
begin{array}{l}
text{(1) unitary symmetric fusion category}\
text{(2) unitary modular category}
end{array}
right.
$$
 The center construction of spherical fusion category defines a modular tensor category.
Please feel free to make comments and give a list of advices.