CatDat

locally finitely presentable

A category is locally finitely presentable if it is locally essentially small*, cocomplete, and there is a set SS of finitely presentable objects such that every object is a filtered colimit of objects in SS. This is the same as being locally 0\aleph_0-presentable.
*Many authors assume the category to be locally small, but this is inconvenient since then locally finitely presentable categories would not be invariant under equivalences of categories.

Relevant implications

Examples

Counterexamples

Unknown

For these categories the database has no info if they satisfy this property or not.