Category theory is the language of diagrams; it studies math from that perspective. However, it turns out that category theory is equivalent to type theory (ie, what computers use). So the reason why diagrams can be reliably used to represent the semantics of type theory expressions is category theory.
My workflow of developing ubiquitous language with clients and then converting that into a diagram mapping classes of things and their relationships followed by translating that diagram into typed statements expressing the same semantics is applied category theory.
The “category theory types” are just names for patterns in those diagrams.
Trying to understand them without first getting that foundational relationship is the path to frustration — much like reading GoF before groking OOP.