The Cauchy completion of an object $X$ is a universal way to make it “Cauchy complete”. There are different (overlapping) meanings of “Cauchy complete”, corresponding to different notions of “Cauchy completion”:
The Cauchy completion of a space is a complete space.
The Cauchy completion of a category is the Karoubi envelope of the category.
The Cauchy completion of an enriched category is a Cauchy complete category.
The Cauchy completion of an (infinity,1)-category is an idempotent complete (infinity,1)-category.
Last revised on August 15, 2023 at 14:52:47. See the history of this page for a list of all contributions to it.