Applications of Concrete Categories in Computer Science

Question

From Wiki:

"In mathematics, a concrete category is a category that is equipped with a faithful functor to the category of sets. This functor makes it possible to think of the objects of the category as sets with additional structure, and of its morphisms as structure-preserving functions. Many important categories have obvious interpretations as concrete categories, for example the category of topological spaces and the category of groups, and trivially also the category of sets itself." http://en.wikipedia.org/wiki/Concrete_category

Question: Are applications of category theory in computer science based primarily on the use of concrete categories?

Answer 1

In the programming language Haskell, the category Hask is the category with Haskell types as objects and functions between types as values. A functor from Hask to Set is one that takes each type to a set of each possible value to that type and functions to functions. This is concrete.