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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeSep 24th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexSince the question came up again on MO (<a href="http://mathoverflow.net/questions/39802/homotopic-quotients-of-simplicial-sets-as-infinity-groupoids/39849#39849">here</a>) I added to [[coimage]] a bit on the $\infty$-version.

   Since the question came up again on MO (here) I added to coimage a bit on the $\infty$-version.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeFeb 2nd 2017
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexOnce again on [MO](http://mathoverflow.net/questions/261021/monomorphisms-epimorphisms-co-images-and-factorizations-in-infty-categori). Do we really want to continue bowing to the tradition of using "coimage" for the (mono, regular epi) factorization and "image" for its dual? It's quite understandably confusing. What if we just redirect [[coimage]] to [[image]] (and copy non-duplicated content over), since the latter already contains the nice paragraph: > Note that some authors drop the “regular” and simply call these constructions the image and coimage respectively. This can be confusing, however, since in many cases (such as in any regular category) the regular coimage coincides with the $M$-image for $M=Mono$ the class of all monomorphisms, which it is also natural to simply call the image.

   Once again on MO. Do we really want to continue bowing to the tradition of using “coimage” for the (mono, regular epi) factorization and “image” for its dual? It’s quite understandably confusing. What if we just redirect coimage to image (and copy non-duplicated content over), since the latter already contains the nice paragraph:

   Note that some authors drop the “regular” and simply call these constructions the image and coimage respectively. This can be confusing, however, since in many cases (such as in any regular category) the regular coimage coincides with the $M$-image for $M=Mono$ the class of all monomorphisms, which it is also natural to simply call the image.