is their a preposition

No, “their” is not a preposition. It is a possessive pronoun (or possessive determiner).

Function of “Their” as a Possessive Pronoun/Determiner:

1. Indicates Possession or Ownership
   • Their restaurant is very popular.
   • The chefs take pride in their work.
2. Used Before a Noun
   • Their new menu features local ingredients.
   • Customers love their quick service.

Why “Their” Is Not a Preposition

• Prepositions (e.g., in, on, under, about) show relationships between words.
• “Their” does not function this way; it indicates possession, making it a possessive pronoun/determiner.

Thus, “their” is a possessive pronoun, not a preposition.