The Azimuth Project
Set theory for category theory

Vopěnka’s principle

Some categorical forms of Vopěnka’s principle are listed:

  1. No locally presentable category has a large discrete full subcategory.
  2. Every complete or cocomplete category with a small dense full subcategory is locally presentable.
  3. Every category with a small dense full subcategory is well-copowered.