You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Morgan Rogers (he/him) (May 22 2026 at 14:49):We can define the left or right Kan extension of one functor along another when they share a domain. What are the corresponding notions for functors sharing a codomain (link is to a diagram in quiver)?
Ruby Khondaker (she/her) (May 22 2026 at 14:51):Kan lifts, right? As far as I know they aren’t as well studied because they exist far less frequently than kan extensions.
Ruby Khondaker (she/her) (May 22 2026 at 14:54):I’d recommend checking out section 2.1 of @fosco ‘s “coend calculus”, here’s a snippet to whet your appetite:
image_BC2D70EA-AEC0-4D38-A959-56BD40027ECB_1779461693.jpeg
Morgan Rogers (he/him) (May 22 2026 at 15:05):Ah, now that I have the name I see that they're mentioned early on the nLab page for Kan extensions, I had just missed it in scanning. Thanks Ruby!
David Corfield (May 22 2026 at 15:51):Years ago, we had an n-Category Café discussion on the comparative infrequency of Kan lifts.
Nathanael Arkor (May 24 2026 at 06:51):It's not true that "Kan lifts" are less common than Kan extensions. It is just that they are essentially coextensive with [[relative adjunctions]], so you will far more literature referring to the latter than the former. You will find a discussion of this in The formal theory of relative monads in the section on relative adjunctions.
Ruby Khondaker (she/her) (May 24 2026 at 10:13):Ah i see, apologies for my inaccuracy
Morgan Rogers (he/him) (May 24 2026 at 21:18):This coincidence is great news, thanks for pointing it out @Nathanael Arkor