Not signed in (Sign In)

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

  • Sign in using OpenID

Discussion Tag Cloud

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

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeMay 15th 2011

    New entry universal epimorphism redirectinig also universal monomorphism. It is not among those variants listed in epimorphism. We also do not list absolute epimorphism (epimorphism which stays epimorphism after applying any functor to it). Every split epimorphism stays split after applying a functor hence it is absolute, but is there a counterexample of an absolute epimorphism which is not in fact split ?

    By the way, here is an archived version of the old query from strict epimorphism

    David Roberts: I’m interested in a bicategorical version of this. You haven’t happened to have done this Mike?

    Mike Shulman: Not more than can be extracted from 2-congruence (michaelshulman) and regular 2-category (michaelshulman). What is there called an “eso” is the bicategorical version of a strong epi (which agrees with an extremal epi in the presence of pullbacks), and what is there called “the quotient of a 2-congruence” is the bicategorical version of a regular epi. I’ve never thought about the bicategorical version of a strict epi; since strict epis agree with regular epis in the presence of finite limits I’ve never really had occasion to care about them independently.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeMay 17th 2011

    Any absolute epimorphism is split. If e:XYe\colon X \to Y is absolute epi, then it is preserved by Hom(Y,)Hom(Y,-) and so Hom(Y,X)Hom(Y,Y)Hom(Y,X)\to Hom(Y,Y) is surjective, hence 1 Y1_Y is in the image of some s:YXs\colon Y\to X, which must be a section of ee. Cf. also absolute coequalizer.

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeMay 17th 2011

    Oh thanks, I like the argument!

    • CommentRowNumber4.
    • CommentAuthoreparejatobes
    • CommentTimeMar 6th 2012

    I’ve added this to both split epimorphism and split monomorphism.

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeMar 7th 2012

    I redid the definitions and terminology in these sections, keeping what Eduardo wrote and adding more.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)