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Stream: learning: questions

Topic: name for category of arrows inverted by a functor

Jonas Frey (Sep 01 2025 at 15:12):

Is there a name for the type of 2-categorical finite weighted limit which in Cat characterizes the class of arrows inverted by a given functor $F : A \to B$? I think it can be expressed as the inverter of $F\circ\eta$, where $\eta:P\to Q:A^𝟚\to A$ is the canonical 2-cell between the two projections out of the arrow category $A^𝟚$.

This kind of limit is similar to a kernel pair, more precisely I think it is dual to coinverters in the same way that kernel pairs are dual to coequalizers.

Mike Shulman (Sep 01 2025 at 15:25):

[[generalized kernel]] claims this is sometimes called an "invertee".

Jonas Frey (Sep 01 2025 at 15:32):

Haha, and from the nlab edit history it seems that it's you who put it there (v1, May 2010)! With an attribution to a seminar talk by Garner.

Jonas Frey (Sep 01 2025 at 15:34):

Google doesn't find any occurences of "invertee" apart from the nlab, but I like it.

Mike Shulman (Sep 01 2025 at 16:46):

I suspected it might have been me, but didn't have time to check the edit history. (-: