There are a few very useful websites when it comes to either finding a specific object with certain properties (and maybe lacking other properties) or finding out which properties a certain object has. For example, there are $\pi$-Base and Topospaces for topological spaces (the former having an amazingly powerful search language). I suppose on a more classical level there is also the Atlas of Finite Groups for (as one would hope) finite groups.
Is there a similar reference (website, article, book, etc.) for categories? That is if I want to know if a certain category is complete, or admits a monoidal structure, or if I want an example of a locally-small-but-not-small category, is there somewhere where I can look such things up. I've done a fair amount of looking for such a thing but have not found one so far. I know that the nLab often has information, but it often goes far beyond what I need and omits some of the more basic things.