Catalysts are Currency items that are exclusive drops from the Breach mechanic. Catalysts add Quality that affect certain modifiers on items. There are two categories of Catalyst, one that affects Jewellery and one that affects Jewels.
Weapon, Armour, Belt, and Jewellery Items are Equipped to the character in the Inventory Panel. Flasks, Skill Gems, and Jewels are never considered to be Equipped.