A category with pullbacks clarification

Question

In my opinion, one of the difficulties in category theory for beginners is the terminology. I have come across the following sentence in the internal category definition.

"An internal category in a category $C$ with pullbacks is an internal precategory in $C$ such that the diagram formed by $d,c,p,q$ is a pullback."

I am familiar with the definition of an internal precategory in $\mathcal{C}$. My questions is the "with pullbacks" part. I would like to know if

1. The sentence talks about $C$ being with pullbacks, or
2. There is a thing called "an internal category with pullbacks".

My intuition points towards 1, but I do not know what it means by a category with pullbacks (I am familiar with the definition of a pullback). Does it mean any category with at least one pullback?

Any help or advice will be greatly appreciated.

Answer 1

A category with pullbacks is a category in which the pullback of ANY pair $X \rightarrow Y \leftarrow Z$ exists.