nLab
lifted limit

Contents

Contents

Idea

A functor F:𝒞𝒟F\colon \mathcal{C}\to \mathcal{D} is said to lift limits of a particular shape II if for any diagram J:ICJ:I\to C, any limiting cone for FJF \circ J in 𝒟\mathcal{D} is the image of a limiting cone for JJ in 𝒞\mathcal{C}.

Terminological remarks

Lifting limits is closely related to creating them. The relationships between these notions were the subject of a post by Aleks Kissinger at the categories mailing list, here, but there is some dispute about its correctness.

Last revised on August 28, 2017 at 19:00:05. See the history of this page for a list of all contributions to it.