Who gave the opus numbers to Beethoven's pieces?

The opus numbers for Beethoven's compositions were assigned by his publisher, Franz Anton Hoffmeister, and later by other publishers. The numbering system was established to catalog Beethoven's works and help manage their publication. However, not all of Beethoven's compositions were given opus numbers; some were published posthumously and received "WoO" (Werke ohne Opuszahl) designations instead.