Defining the cosmos: Properties and definition
This post is part two of a little two-part miniseries about defining the cosmos. To learn what a cosmos is in mathematics, or rather what we want it to be, you can read the first part. There we described a cosmos as a nice place to enrich a category, or a nice place to do enriched category theory, and to quickly recap, an enriched category is a category where we have objects of morphisms instead of just a collection of them, and these objects come from some monoidal category. In this post we will continue the story, and focus more on the definition rather than the setup. ...