In Category Theory, functoriality refers to the property or concept that a functor preserves the structure and relationships between objects and morphisms in categories. More specifically, it means that if there is a morphism between two objects in one category, then there is a corresponding morphism between their images under the functor in another category, and these morphisms preserve composition and identities. Functoriality is a fundamental property of functors and plays a crucial role in relating different categories and studying their properties. It allows for the translation of concepts, properties, and structures from one category to another through the use of functors.