Pointed topological spaces

Even though this blog is not centered around a specific topic, we have during the last year looked more frequently at certain topics than others, such as (co)homology theory, homotopy theory and category theory. We will continue this trend today as we will try to find a solid reason for a particular object to exist. These objects were briefly mentioned in the earlier post on tensor triangulated categories, namely spectra. These objects are hugely important to the field of algebraic topology, one reason being that they are intimately linked to cohomology....

Since one of my main mathematical interests is homotopy theory, im bound to often bump into things that require the use of base-points. This has long been the classical way to study spaces, especially in terms of homotopy groups. When I was introduced to these so-called pointed spaces, I couldn’t help but feel that these we less natural, or more ad hoc, than regular spaces. I didn’t know much about categories then, but have since learned it is usually in this context that some form of naturality occur....