These three types of functors correspond to [stuff, structure, and properties](https://ncatlab.org/nlab/show/stuff,+structure,+property)!! So we have a correspondence between

- only adding capabilities is the same as forgetting purely properties
- only changing the underlying set and forgetting purely structure
- only discovering a new kind of resource and forgetting purely stuff

Hmm... now I have to think about why these correspondences make sense! This is very fun!