Under Category

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. It turns out that pointed spaces actually come from a very nice natural categorical construction, which of course is the focus of this post. I will assume introductory knowledge of categories, and I will try to keep this short for once. ...