Hyponymy is not restricted to objects, abstract concepts, or nouns. It can be identified in many other areas of the lexicon. 

E.g. the verb cook has many hyponyms.
Word: Cook
Hyponyms: Roast, boil, fry, grill, bake, etc.

Word: color
Hyponyms: blue, red, yellow, green, black and purple.

In a lexical field, hyponymy may exist at more than one level. A word may have both a hyponym and a super ordinate term.

For example, 
Word: Living
Hyponym: bird, insects, animals

Now let's take the word bird from above hyponyms.
Word: Bird
Hyponyms: sparrow, hawk, crow, fowl

We thus have sparrow, hawk, crow, fowl as hyponyms of bird and bird in turn is a hyponym of living beings. So there is a hierarchy of terms related to each other through hyponymic relations. 

Hyponymy involves the logical relationship of entailment. E.g. 
'There is a horse' entails that 'There is an animal.'

Hyponymy often functions in discourse as a means of lexical cohesion by establishing referential equivalence to avoid repetition.