§ Locally Presentable Category
- A category is locally presentable iff it has a set of objects such that every object is a colimit over these objects. This definition is correct upto size issues.
- A locally presentable category is a reflective localization of a category of presheaves over . Since is the free cocompletion, and localization imposes relations, this lets us write a category in terms of generators and relations.
- Formally, :
- 1. is locally small
- 2. has all small colimits
§ Reflective localization
§ Accessible Reflective localization