Could someone please indicate a website, book or PDF that contains a catalog of categories? I am looking for a place that contains descriptions and properties of the best known categories. I am currently interested in the following categories:
- Category of Manifolds ($\mathbf{Man}$)
- Category of Smooth Manifolds ($\mathbf{Diff}$)
- Category of Topological Spaces ($\mathbf{Top}$)
- Category of Open Subsets of a topological space $X$ ($\mathbf{OpenSets}(X)$)
- Category of Algebras
I always have trouble finding a good description and properties of a certain category in which I am interested. That's why I'd like to know if there's a place that contains the descriptions and properties of the best known categories.
The best references I found are the following:
- Categories in category theory
- Database of Categories
- Category Theory in Context. On page 229 there is a catalog of categories. However, some categories in this catalog have only been cited briefly.
Thank you for your attention!