I'm just getting started with playing with yeast. I did my first two starters this weekend. I don't dare yet to repitch yeast as I have my head full with basic processes, kegging, keezers and now lagers. But yeast management is on my next steps along with water management.
I wonder if liquid yeast can be cultured at home? Can you buy some yeast and create the conditions to just grow it and use it at will? So far I only heard of people repitching until the yeast is too weak...
Yes! Yes you can.
It comes down to how much effort and expense/equipment you want to put into it. I build starters bigger than needed, then pour off a pint to keep in the fridge. Many months later, I can pull a jar and make a new starter to use that yeast again, and again I will save some of the starter in the fridge for next time.
You can do this as many times as you feel comfortable. The yeast may change over many generations, or get contaminated, but generally they can be used quite a few times if you are careful with sanitation.
Reusing yeast could be as simple as making a batch of low ABV beer, and then putting a big beer on the yeast cake when the first beer in done.
Some people like to scoop yeast out of the yeast cake from a finished batch, and either wash it, or save it as-is. I do not like this method, but others do so you should look into it while checking out this topic.
If you really want to go all in, you could learn about making slants, freezing yeast, growing them up from single colonies on plates, and on and on. You have to decide at what point "fun hobby" turns into "too much work", and only you can decide that. Collecting and maintaining a library of yeast samples could be a hobby of its own.