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.
    • CommentAuthorUrs
    • CommentTimeJul 1st 2017

    At interactions of images and pre-images with unions and intersections I have added pointer to Lawvere 69 and there at Adjointness in Foundations I added a bit more text and cross-references.

    • CommentRowNumber2.
    • CommentAuthorVitalyR
    • CommentTimeFeb 7th 2021
    I'm reading this article, and find a little contradiction between the text and formula in the properties 2. of Proposition 2.1.
    Should "contained in" be removed in the explanation of the properties 2. of Proposition 2.1?
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 7th 2021

    Let me see… It looks okay to me: The intersection of images may be larger than the image of the intersection.

    In an extreme case, take S 1S_1 and S 2S_2 to two disjoint copies of the same non-empty abstract set, and each with the same image under ff. Then the image of the intersection is empty (because the intersection itself is), but the intersection of the images is the image of either subset.

    Hm, now I see that this same point is also amplified in a comment right below.

    So maybe I am missing your point?

    To make sure we are looking at the same part of the entry: You can copy and paste the relevant code from the entry to the Forum here. (Just make sure you check the radio button “Markdown+Itex” below the edit pane here.)

    • CommentRowNumber4.
    • CommentAuthorVitalyR
    • CommentTimeFeb 10th 2021
    Sorry I should refer to Proposition 2.2 in the last comment. I remove "contained in" in Proposition 2.2, see the diff:

    Now everything there should be OK.

    I love nLab! Thanks for your great work!
    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeNov 29th 2021
    It seems to me that the equality in Proposition 4.1 requires the function, f, to be injective. An arbitrary function, f, gives us that the RHS is a subset of the LHS.
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 30th 2021
    • (edited Nov 30th 2021)

    Just to highlight that the question is about the “projection formula” here which was apparently added by Todd Trimble in rev 10 (leaving the direction under question now as “to be continued”).

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeDec 1st 2021

    For what it’s worth, the statement in question (here) is also stated as Exercise A.4(k) in Lee 2000.

    diff, v19, current

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)