[foldU]

This is correct, I appreciate you for putting it so coherently :). I think I didn’t make it clear enough in the piece that I’m coming from a stance of fast access being table stakes, and the question being about how that’s accomplished.

[necovek]

"Caching" is an idea of storing a result of an expensive computation in storage that is faster to get from than doing the original computation (in very generic computer terms, computation can be simply fetching from the network or slower local storage).

What you describe as "caching algorithms" are not really caching algorithms, but cached object lifetime management algorithms (LRU, LFU...).

"Abstraction" is a higher level, simplified view of a set of concepts, yet caching is a single concept. See eg. https://en.wikipedia.org/wiki/Abstraction_(computer_science)

It sounds like you are both trying to redefine what "caching" means (tying it to implementations of particular algorithms), but also what "abstraction" means.

We should be very deliberate with the language we use, and our main goal should be to make it simpler to understand, not harder — I believe you are doing the latter here.