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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMar 9th 2012
• (edited Mar 9th 2012)

have added to codomain fibration a brief paragraph on the $(\infty,1)$-version here and that it’s a coCartesian fibration.

• CommentRowNumber2.
• CommentAuthorT
• CommentTimeMay 16th 2020

Correction of the form of cod in terms of the hom functor. Original notation would have referred to taking the hom in C and using the second spot in the hom functor as an argument. (Rather, cod is an arrow between Cat-homs, and as such is a value of the hom functor on a pair of arrow(s) of Cat, not a partially applied instance of a hom functor.)

• CommentRowNumber3.
• CommentAuthorAlec Rhea
• CommentTimeMar 3rd 2021

Added discussion of the subobject fibration, viewed as the fibered skeleton of the monomorphism subfibration of the codomain fibration.

1. The section on subobject fibration introduces new notation for the arrow category (C with an arrow superscript) without explanation.
• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMay 26th 2022
• (edited May 26th 2022)

It was maybe not quite undefined, since it said that it’s the domain of the codomain fibration, but I have added a parenthetical remark for clarity (here).

(You are invited to make such small – or even large – edits yourself, when you see the need: Just hit “edit” at the bottom of a page. Typically that’s more efficient than trying to make somebody else do it.)