Monkeys can be found roaming freely even in the city. They are revered because the Hindus worship a monkey general, Hanuman, who in the Indian epic poem, Ramayana, commanded an army of monkeys to fight for the hero, Rama. This is not the same monkey god, Sun Wukong, in the Chinese literary classic, "Journey To The West."
Interestingly, I have never seen a cat in New Delhi and here. Perhaps, fish is not easily available as New Delhi is situated in the centre of the Indian continent and far from the coasts.