In this talk I am going to start with generalizing complete Segal spaces, which is a model for higher categories, to the notion of complete Segal objects. This is a way to define higher category objects internal to other higher categories. With the help of complete Segal objects we can give meaning to "representable functors valued in higher categories". Using representability we can study certain important functors and explain how they give rise to "n-univalent maps", which is a chain of n maps generalizing the notion of univalent maps. Finally, I will discuss how studying these n-univalent maps can help us understand aforementioned functors.