Topological functors I: definition, duality, limits and colimits

I have briefly mentioned topological functors in a recent post. It is time for me to explain what they are. This is a truly wonderful concept, which abstracts topological spaces away and concentrates on the key properties of the forgetful functor from Top to Set. In other words, that forgetful functor is topological, but there are many others, including some involving streams, prestreams, and d-spaces. We will see some of the classical properties of topological functors, notably that topological functors are self-dual, and that they preserve and create both limits and colimits. Read the full post.