I have some free time and I want to use it to revise product spaces from a general/universal perspective. Coming from Analysis and coming across them all the time (I feel so atleast), I am willing to study the necessary basics of algebra/category theory needed for getting a bird's eye view of e.g.
arbitrary (infinite) product measure spaces and product measures, independency and arbitrary tensor products (I recall having read that there was a reason for tensor product and product measure notation both using the symbol $\otimes$)
direct product and sum in an arbitrary setting and why the finite-dimensional vector space case is so special, i.e. why for matrices column rank equals row rank in the language of the product spaces and categorical duals
I am thankful for every recommendation of books, articles, blog entries etc. and comments related to this topic.