Sure is! Batman has been a staple of DC Comics for a long time. His stories and adventures are part of the DC universe. DC has built a rich and complex world around him.
Batman would probably isolate himself at first. He'd retreat to the Batcave to analyze the situation. He might feel a sense of guilt, thinking he should have seen the betrayal coming. After that, he'd start planning his counter - move. He'd use his vast resources and knowledge to expose the truth behind the betrayal and take down whoever is behind it.
There are a ton of Batman DC comics. Different publishers, storylines, and reprints make it impossible to say exactly how many. But you can bet it's a huge number!