Inherently ambiguous CFLs and the DCFL / unambiguous-CFL / CFL hierarchy

Ambiguity is a property of a grammar (a string with $\ge 2$ parse trees); inherent ambiguity is a property of a language (every grammar for it is ambiguous). These nest into a strict chain $\text{Regular}\subsetneq\text{DCFL}\subsetneq\text{Unambiguous CFL}\subsetneq\text{CFL}$: every deterministic CFL is unambiguous, but some CFLs are inherently ambiguous and lie outside even the unambiguous class.