David Spivak offers an account of Categories as database schemas with path equivalencies that is similar to the account you’ve given here in his book Category Theory for the Sciences. He still presents the traditional definitions, giving examples mainly from the category of sets and functions. I also didn’t find his presentation of database schema definition especially easy to understand, but it is very useful when you realize that a functor is a systematic migration of data between schemas.
David Spivak offers an account of Categories as database schemas with path equivalencies that is similar to the account you’ve given here in his book Category Theory for the Sciences. He still presents the traditional definitions, giving examples mainly from the category of sets and functions. I also didn’t find his presentation of database schema definition especially easy to understand, but it is very useful when you realize that a functor is a systematic migration of data between schemas.