Cut papaya into four slices that run up and down the fruit. Then, remove the skin and seeds of the fruit. Finally, cut into small slices. In a large pot, place a layer of papaya and then a layer of sugar. Continue to do this until there is no more papaya or sugar. Place in the refrigerator overnight. The next day, add cinnamon sticks and cloves and cook on the stovetop until the papaya is cooked and the sugar turns into a light syrup.