Category Theory Vs. Topology
Here's the dirt on how these objects relate to one another:
Topological spaces (in the most abstract point-set sense) form a category, whose morphisms are the continuous maps.
Certain algebraic topological transformations, such as the fundamental group operation, provide some of the most natural examples of functors.
Certain algebraic topological transformations, such as the fundamental group operation, provide some of the most natural examples of functors.