Add more properties of categories #18
Description
As of writing this, CatDat already has 79 properties of categories, but there are many more which are well-known and should be added at some point. IMPORTANT: for each of these, according to the contribution guidelines, one should then also add relevant implications and also decide which categories have this property and which don't. Because of this, this is quite a bit of work. Maybe one can do one commit (or PR) per property.
- regular
- Barr-exact
- extensive
- generating set
- pullback-stable coproducts
- accessible
- total
- cototal
- gaunt
- images
- coimages
- subterminal object
- concretizable
- filtered / cofiltered
- quasi-topos
- has dense small subcategory
Further properties which probably are not so relevant for now:
- pre-abelian
- pseudo-abelian
- semi-abelian
- quasi-abelian
- semisimple abelian