Auxiliary Adjectives

In Japanese, auxiliary adjectives are auxiliaries that work like adjectives. This single English term, "auxiliary adjective," has been used to refer to various things in Japanese, like:

1. hojo-keiyoushi 補助形容詞
   "Support adjectives."
   Adjectives that come after the te-form of a verb, or after the adverbial form of an adjective.
   Example: in tabete-hoshii 食べてほしい, "[I] want [you] to eat [it]," the auxiliary adjective hoshii ほしい.
2. fukugou-keiyoushi 複合形容詞
   "Compound adjectives."
   The ones where an adjective is attached to the noun form of a verb.
   Example: in tabe-yasui 食べやすい, "easy to eat," the auxiliary adjective yasui やすい.
3. jodoushi 助動詞
   "Helper verbs."
   The ones which inflect like adjectives.
   Example: in tabetai 食べたい, "want to eat," the ~tai ～たい suffix.
4. The adjective ii いい.
   Just... the adjective ii いい. And its conjugations.
   It doesn't fall in any of the categories above, but it's practically an auxiliary.
   
   

In Japanese, the term hojo-keiyoushi is sometimes used to refer to words that aren't technically hojo-keiyoushi. As far as I know, only hoshii, and perhaps nai ない, are hojo-keiyoushi. Everything else is something else.