Exemplary idea Alex,
Your vision is indeed a natural endgame to our current world wide dilemma. Upon reading your post, I employed some GoogleFu (modest effort, left handed only):
http://science.sciencemag.org/content/352/6291/1312
and here's a version for the kids:
https://www.sciencealert.com/scientists-have-figured-out-how-to-turn-co2-into-solid-rock-within-months
Perhaps your had read this in passing, and recollected it somewhat later. Perhaps original thought? Not to worry
Are you always right too? Same here. I'm glad we agree!
Bonus points if these gurus can make reprocessed building materials out of it. As for the oxygen, we have plenty of uses for that industrially, so nothing wrong with an additional cheap supply via a by-product.
I was rummaging in the local tip one day (don't ask, it's an old pastime). And was thinking about the currently fictional cliche of "grey goo" nanobots reprocessing the contents of the refuse.
Pour on tamed goo, activate, and tomorrow one has neat stacked cubes of dominant elements or compounds from the refuse.
...Then to deactivate the bots in the pit before they reach China...