Omega
The last sat of a whole bitcoin: a sat s where s + 1 is divisible by 100,000,000. On its own it is not a category; combined with others it is.
How a sat qualifies
Ordinal theory numbers sats from 0, so the sat numbers fall into runs of 100,000,000, one per bitcoin. Sat s is an omega when it ends such a run: s leaves a remainder of 99,999,999 when divided by 100,000,000, so s + 1 is divisible by it. The sat right after an omega is always an alpha.
The first omega is sat 99,999,999, the last sat of the first bitcoin. Exactly 20,999,999 omegas will exist, one fewer than alphas: the last bitcoin of the numbering, from sat 2,099,999,900,000,000, will only ever have 97,690,000 sats, so it never gets its last one.
Omegas and blocks
The last sat of a block is an omega exactly when the next block begins with an alpha. Every block from 0 to 419,999 ends on a whole bitcoin, so its last sat is a black omega (or a black rare or black epic one); after that, fewer blocks do at each halving, and from block 2,100,000 on none. Most omegas fall mid-block.
An omega just before a round number of bitcoin also carries a milestone type: kilosat, decasat, centasat or megasat, worked out on s + 1.
On this site
There is no plain Omega category: an omega with no other type is not tracked. Omegas are tracked where they combine with something else: the last sat of a block (Black omega), a milestone, or a historic place such as vintage, Nakamoto blocks, pizza or Silk Road. Those categories are listed below.