The time is takes for a cat to decompose is dependent upon factors such as location of the body, access to the corpse by predators and others and body fat percentage. Due to these differing factors, a body could take a few weeks to decompose or years to decay.
All bodies go through the same stages of decomposition despite having different factors determining their decomposition time. The first stage of decay is the fresh stage. During this stage, it is unlikely to see any outward change in the body. Not long after the first stage ends is the second stage, which is often called the bloat stage. During the bloat stage, a body begins to bloat or puff up and look recognizably different than it did during the fresh stage.
Active decay is the next stage, and during this stage, a deflation of the body occurs as well as a noticeable stench. After active decay, advanced decay, which entails the majority of the flesh having decayed off of the corpse, sets in. Lastly comes the dry decay stage. This is the stage that is most easy to recognize. In this stage, the remains are mostly bone with only a small bit of dried skin remaining. This ends the stages of decomposition.