I heard Taiji is a fighting art, is that true?

Yes absolutely. It is hard to see it when you see a group of elderly people doing the forms at a very slow manner and in a fuller non aggressive attitude, and usually these days many people are not taught the fighting concepts of the art. I have heard people advertise Taiji as the peaceful martial art. I have also heard of people who take up the art because it does not involve combat, nothing could be further from the truth. Taiji does promote inner peace, and quietude, but it's fighting applications are some of the most scientific, and some might say most vicious of all martial arts. While the numbers are far less, there are those that still understand the true nature of the art today. Taiji quan is a complete art, and it's gifts in all areas can only be realized if it is fully investigated and understood, cutting oneself off from one part of the learning is detrimental, and restricts a practitioner from ever attaining the highest levels. I am not saying one must learn to fight and then go around killing people, but knowledge of fighting in the art opens up subtle doors in the more peaceful aspects that may not have been seen in a more basic study.