LN fit better in the idea. Cashu is more like vouchers.
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LN is part of it (and a rail that Cashu uses too). Cashu mints are like banks. They accept collateral (Bitcoin) and issue tokens (vouchers / “bank notes”) for that collateral.
They “could” conceivably be fractional, and as Hal rightly said, people may trust/value tokens from one mint less than another.