# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorMike Shulman
• CommentTimeMay 3rd 2021

When we say

A category $C$ is cofinally small if there is a small category $C_0$ and a cofinal functor $C_0 \to C$.

does “cofinal functor” mean “final functor” or “co-(final functor)” i.e. “initial functor”?

The only links to this page I can find are from calculus of fractions, where my guess would be that what’s meant is “initial functor”, and from ind-object, where my guess would be that what’s meant is “final functor”. So I don’t know.

• CommentRowNumber2.
• CommentAuthorRichard Williamson
• CommentTimeMay 3rd 2021
• (edited May 3rd 2021)

I think that ’final functor’ is the almost universal meaning in the literature; in fact, whilst I’m writing this quickly, I would have thought this is also what is meant at calculus of fractions?

What a terribly confusing piece of terminology!

• CommentRowNumber3.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 3rd 2021
• (edited May 3rd 2021)

This was discussed here: https://nforum.ncatlab.org/discussion/9054/final-functor/.

Apparently, Borceux’s Handbook of Categorical Algebra and Lurie’s Higher Topos Theory use “cofinal functor” for the concept that all other books call “final functor”.