Definition
Let be an infinite regular cardinal and let be a category. An object of is called -presentable if the Hom functor preserves -directed colimits. The category is called -accessible provided that :
- has -directed colimits
- has a set of -presentable objects such that every object of is a -directed colimit of objects of
A category is called accessible if is -accessible for some infinite regular cardinal .
A -presentable object is usually called finitely presentable, and an -accessible category is often called finitely accessible.
Read more about this topic: Accessible Category
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