Category of graphs. Hello, I'm writting something about Malcev categories and monadicity. The fact is that I need to know if Graph is or not complete (have all finite limits). It seems easy but I would like a real answer (not my feelings saying that it is) and I don't find that information anywhere.
Thank you for your answers.
 A: First let me just mention that complete usually means "has all small limits". If you want to say "has all finite limits", you could use the term finitely complete or just has finite limits.
You did not explain which particular category of graphs you are talking about, but luckily almost any reasonable choice will have an affirmative answer: yes, the category of graphs has finite limits. I can tell you why if you tell me what objects and morphisms you have in mind.
A: Consider the category G that has exactly two distinct objects (call them a and b) and two distinct arrows a->b. A graph is precisely a functor G -> Set. This means that the category of graphs is a presheaf category. The rest follows.
A: Here's another one: The category of graphs is a topological category over SET an therefore complete and cocomplete.
A: It has all finite products, and I think (depending on your defintion of Graph), it is easy to show that it has equalizers, and thus all finite limits.
If you are talking about directed graphs, then this is the topos of presheaves of sets over the category which consists of a pair of parallel arrows, and thus has a slew of wonderful properties, finite limits included.
