Let $\mathbf{C}$ and $\mathbf{D}$ be to categories, $F: \mathbf{C} \to \mathbf{D}$ a functor and $X \in \mathbf{C}$ an object. My task is to construct an induced functor $F/X: \mathbf{C}/X \to \mathbf{D}/FX$
My first question is if $\mathbf{D}/FX$ is a typo, shouldn't it be just $\mathbf{D}/X$? If so, what restrictions do I have in my construction regarding the word "induced",does this mean I have to construct a functor that inherits the properties of $F$ as a functor?