Of course cats can be trained!
Here is an example:
People often think that cats can’t be trained. This may be due to the use of punishment and aversive techniques that have been incorporated into much of our animal training in the past.
Nowadays, with understanding that positive reinforcement is a superior means of teaching animals, we are realising that so many species can be motivated to perform behaviours we want from them.
Marine mammals in captivity and captive zoo animals are often part of positive reinforcement training programmes that enrich their lives while enabling us to work with them more safely. Indoor cats can also have their lives enriched and us pet owners benefit from training them to listen to us: we have a better bond with our pet AND we can utilise the training to enable us to perform routine tasks that they may not have otherwise enjoyed, such as grooming and teeth brushing.