Preservation of limits
A functor G is said to preserve all limits of shape J if it preserves the limits of all diagrams F : J → C. For example, one can say that G preserves products, equalizers, pullbacks, etc. A continuous functor is one that preserves all small limits.
Do limits and Colimits commute?
In general, limits and colimits do not commute.
What is a functor category?
From Wikipedia, the free encyclopedia. In category theory, a branch of mathematics, a functor category is a category where the objects are the functors and the morphisms are natural transformations between the functors (here, is another object in the category).
