What does Variance of Functor mean? I have to show that composition of two functor is covariant if the two functor has same variance, and composition of functors is contravariant if they have different variance.
Functors map both objects and morphisms. Covariant functors preserve morphism composition: $F(f \circ g) = F(f) \circ F(g)$. However, contravariant functors reverse this composition: $F(f \circ g) = F(g) \circ F(f)$.
So if you compose two functors of the same variance, you'll either get preserve + preserve = preserve or flip + flip = preserve (flip twice and you're back in order).
On the other hand if two functors have opposite variance, you'll have preserve + flip = flip (flipping once and preserve order once will result in flipping the order around).
"Variance" means the same type: either covariant ar contravariant.
So you are asked to show that the composition of two covariant or two contravariant functors is covarient, and that composition of a covariant functor with contravariant (in any order) is contravariant.